Theophrast did not write about this directly in an overly explicit and extensive way, but he indeeds gives several hints on these, in his Characters.
This answer complements @kimchilover's answer.
The institution sought after is ἔρανος (eranos). Which is now often translated as 'loan', 'loan-application' or 'subscription'. That this was first translated/described by scholars like Casaubon as communem arcam/ 'common chest' makes this somewhat difficult to find and follow. But the established institution of eranos is named several times in Theophrast's work, without much fundamentals a the 'grand scheme' of how this worked, but with more some illuminating details in how different people behaved within that framework, and a few hints on what this meant in practice not found elsewhere.
The concept or institution of eranos is properly explained as:
The name is derived from the Ancient Greek word ἔρανος meaning "a banquet to which the guests bring contributions of food, a no-host dinner."
Or in more detail:
Eranos (Greek ἔρανος) in ancient Greece referred to an association that made contributions for a specific purpose, e.g. for the ransom from captivity or slavery, payment of a fine or for a common feast. Eranos was also the name of the collected property and the purpose of the collection (e.g. payment).
Homer used ἔρανος in the Odyssey to denote a simple, ordinary meal with regular participants who contributed to it (Od. 1, 226).
The έρανος in modern Greek means a specific fund-raising or fund-raising action.
In classical Athenian democracy, the Eranos association constituted a separate legal entity from the 6th century BC onwards. The association had the function of a credit union and was set up in accordance with its statutes to provide for the needy. Economic historians therefore see it as a prototype of the insurance system. The Eranos Association included provisions of personal, procedural and property law. In addition, it had active and passive procedural law, i.e. it could sue and be sued.
— de:WP, translated
Since both Wikipedia articles as well as most web searches are dominated by the modern theology association named in this manner, in
The Oxford Classical Dictionary reports:
Eranos was essentially concerned with *reciprocity: at first of food, and later of money. In *Homer, eranos refers to a meal for which each diner contributed a share (Od. 1. 226); alternatively, the venue might be rotated. This earlier meaning was never lost (Xen. Mem. 3. 14. 1); but, by the later 5th cent. bce, the concept had evolved to include a *credit system, common in Athens, whereby contributors lent small sums to help out a common acquaintance in need (Lys. 20. 12; cf. Pl. Ap. 38b). The strong obligation to lend was matched by a reciprocal obligation to repay as soon as possible. The reciprocity inherent in the eranos-idea is reflected in metaphorical usage: to die in battle for the polis was to offer one's kallistos eranos (‘finest contribution’), receiving in return ‘immortal praise’ (Thuc. 2. 43. 1). Readiness to contribute towards eranos loans could be cited in Athenian courts as an aspect of civic virtue (Antiphon 2. 2. 12); failure to repay as indicative of general degradation (Lys. fr. 1 Carey). Disputed is the extent to which eranists in Athens were ad hoc groupings, or fixed associations (see clubs, greek), somewhat resembling friendly societies.
In the New Pauly we read:
Eranos (ἔρανος; éranos).
 Collective fund
 Private association
Etymology uncertain; the word originally meant ‘a meal for friends’ (Hom. Od., Pind.). The cost was borne in common by the participants. Collections made among friends in order to present a gift to one of them were also called éranoi; to give gifts in return was merely customary, not a statutory obligation (Theophr. Char. 17,9). Two legal institutions developed on this basis:
 Collective fund
A kind of collective wealth. Funds (eisphoraí) collected by a group of individuals (plērōtaí, Dem. Or. 21,184f.) were applied to a particular purpose (payment of a fine, payment of a ransom, purchase out of slavery) in favour of a beneficiary. The fund was named after the initiator of its collection: this was often the beneficiary himself. The funds were transferred to the beneficiary purely as an interest-free loan for the purpose stipulated; the members of the fund could take an action for return of the amount (but see Pl. Leg. 11,915e).
 Private association
A particular type of private association was also called eranos; see Associations.
— Thür, Gerhard (Graz), “Eranos”, in: Brill’s New Pauly, Antiquity volumes edited by: Hubert Cancik and , Helmuth Schneider, English Edition by: Christine F. Salazar, Classical Tradition volumes edited by: Manfred Landfester, English Edition by: Francis G. Gentry. Consulted online on 06 June 2022 doi.
This is curious as it lists Characters XVII, but as in kimchilover's answer we read:
6 καὶ φίλῳ δὲ ἔρανον κελεύσαντι εἰσενεγκεῖν εἰπών, ὅτι οὐκ ἂν δοίη, ὕστερον ἥκειν φέρων καὶ λέγειν, ὅτι ἀπόλλυσι καὶ
— Characters. Theophrastus. Hermann Diels. Oxford. Oxford University Press. 1909.
— Thphr. Char. 15.7
Which is about the 'Grouchiness' person, translated in Loeb's Classical Library 225 as:
After first refusing to give to a friend who has asked him to contribute to a loan, he comes to him later and brings it, but adds that he is throwing his money away again.
— J. M. Edmonds: "The Characters of Theophrastus Newly Edited and Translated", William Heinemann: London, 1929.
This character is also translated as "self-centered man" and:
If a friend asks for a contribution to a loan he at first refuses, then comes along with it and says that this is more money wasted.
— James Diggle: "Theophrastus Characters", Cambridge University Press: Cambridge, New York, 2004.
Or in Jebb's translation:
XV. The Surly Man (iii)
Surliness is discourtesy in words.
[…] Then, if a friend asks him for a subscription, he will say that he cannot give one; but will come with it by and by, and remark that he is losing this money also.
Now, the lexicon say on ἔρα^νος , ὁ,:
A.meal to which each contributed his share, picnic, “εἰλαπίνη ἠὲ γάμος ; ἐπεὶ οὐκ ἔρανος τάδε γ᾽ ἐστίν” Od.1.226, cf. 11.415 : metaph., Pl.Smp.177c.
2. generally, feast, festival, Pi.O.1.38 ; “πολύθυτος ἔ.” Id.P.5.77 ; wedding-banquet, ib.12.14, Pherecyd.11 J.; “ἔρανον εἰς θεοὺς..ἐποίεις” E.Hel.388.
II. loan raised by contributions for the benefit of an individual, bearing no interest, but recoverable at law, in instalments, “παρὰ τῶν φίλων ἔ. συλλέξαι” Antipho 2.2.9, cf. Thphr.Char.22.9 ; κομισόμενος τὸν ἔ. recover the loan, Arist.Ph.196b34 ; “ἔ. εἰσενεγκεῖν τινι” Thphr.Char.15.7, Philem.213.14 ; “ἔ. τινι εἰς τὰ λύτρα εἰσφέρειν” D.53.8 ; “ἔ. εἰς ἐλευθερίαν” Id.59.31, cf. GDI2317 (Delph.), al.; “ἔ. ἀναλαμβάνειν” BGU 1165.16 (i B. C., with mention of interest); “ἔ. εἰκοσίμνως” Lys.Fr.19 ; “πεντακοσιόδραχμος” SIG1215.5 (Myconos); “διτάλαντον εἶχες ἔ. [δωρεὰν] παρά τινων” D.18.312 : in pl., debts thus contracted, Ar.Ach.615 (prob.), Hyp.Ath.9 ; τοὺς ἐ. διενεγκεῖν pay off such debts, Lycurg.22 ; ἐράνους λέλοιπε he has left repayment-instalments unpaid, D.27.25 ; ἔ. συνεφήβοις ἀπενεγκεῖν (cf. infr. III) Luc. DMeretr.7.1.
- metaph, τοὐράνου γάρ μοι μέτεστι: καὶ γὰρ ἄνδρας εἰσφέρω (spoken by Lysistrata), Ar.Lys.651 ; “δεῖ τοῖς γονεῦσι τὸν ὡρισμένον ἐξ ἀμφοτέρων ἔ. καὶ παρὰ τῆς φύσεως καὶ παρὰ τοῦ νόμου δικαίως φέρειν” D.10.40, cf. 21.101, Isoc.10.20, Pl.Lg.927c ; “κάλλιστον ἔ. [τῇ πόλει] προϊέμενοι” Th.2.43, cf. X.Cyr.7.1.12, Ph.2.553, etc.: generally, favour, service, esp. one which brings a return, “κάλλιστον ἔ., δοὺς γὰρ ἀντιλάζυται” E.Supp.363 ; “ἔ. ἀντιλαμβάνειν” Arist.Pol.1332b40 ; “ἀποδοῦναι” Alex.280 ; ironically, τὸν αὐτὸν ἔ. ἀποδοῦναι 'pay him back in his own coin', D.59.8.
III. a permanent association apparently religious in character (cf. ἐρανιστής), IG12(1).155.12 (Rhodes, ii B.C.), 22.1369 (Athens, ii A. D.); ἔ. συνάγειν Μηνὶ Τυράννῳ ib.3.74 ; “καλεῖται ὁ αὐτὸς καὶ ἔ. καὶ θίασος” Ath.8.362e ; functioning as a friendly society, Plin.Ep.Trai.92 ; it could apparently lend to a non-member, “ὅρος χωρίων ὑποκειμένων τῷ ἐ. καὶ τῷ ἀρχεράνῳ” SIG1198 (Amorgos, iii B. C.), cf. BGU1133-6 (i B. C.).
Another hint we glean from Theophrast in 22,9 "Parsimony"
10 ἔνδον μένειν, ὅταν ἐκδῷ θοἰμάτιον ἐκπλῦναι: καὶ φίλου ἔρανον συλλέγοντος καὶ διειλεγμένου αὐτῷ, προσιόντα προϊδόμενος ἀποκάμψας ἐκ τῆς ὁδοῦ τὴν κύκλῳ οἴκαδε πορευθῆναι:
Characters. Theophrastus. Hermann Diels. Oxford. Oxford University Press. 1909.
— Thphr. Char. 22.9
is translated as:
If a friend is raising a subscription, and has spoken to him about it, he will turn out of the street when he descries him approaching, and will go home by a roundabout way.
— R. C. Jebb
Or in 'grumbling man'
XVII. The Grumbler (xxii)
… If a subscription has been raised for him by his friends, and someone says to him ‘Cheer up!’ — ‘Cheer up?’ he will answer; ‘when I have to refund his money to every man, and to be grateful besides, as if I had been done a service!’
Similarly, in "I. The Ironical Man (v)", Jebb we see:
To applicants for a loan or a subscription he will say that he has no money; when he has anything for sale, he will deny that he means to sell; or, when he does not mean to sell, he will pretend that he does.
As well as:
XXII. The Mean Man (xxv)
Meanness is an excessive indifference to honour where expense is concerned.
When subscriptions for the treasury are being made, he will rise in silence from his place in the Ecclesia, and go out from the midst.
This he declares is what he contributed to these poor men's subscription-lists, adding that he takes no account whatever of the trierarchies and other state-services he has performed.
— XXIII. Pretentiousness (Loeb)
What can historians make of these?
One type of arbitration, by public officials, has been seen as especially prominent after the 330s when dated lists of public arbitrators start to survive in Attic inscriptions. Eranoi are knonw epigraphically on several Attic horoi from later fourth century and have been inferred at deme level, most recently in the newly-published text of the deme of Kollytos in the 320s. […]
The Characters' eranoi and arbitrations, by contrast, were not promised or allotted in a public assembly. Theophrastus is not alluding to Attica's boards of elderly public arbitrators but to the casual activity of private 'third parties' who might be appealed to at any time during others' disputes. Like the random 'arbitrators' who are sometimes cited in surviving Attic orators, the Affable Man becomes involved, but tries to please both parties: the Tactless Man starts the participants quarrelling again: the Arrogant Man gives his decision while still in the street. So, too, the eranoi conform to those which we meet in the Attic orators, contributions raised by 'collectors' from groups of willing participants and made available to a person in need. They were interest-free, but usually made as loans to be repaid, though not always with such a formal security as we might infer from the examples inscribed on surviving horoi. Repayment was expected, but perhaps not always enforced. 'Be cheerful', the Grumbling Man is told when his friends have arranged such a 'whip-round' for an éranos to him. 'How so,' he replies, 'when I must give the money back to each of them, and besides that, I owe a favour as one who has been done a good turn?' Modern studies of reciprocity could well use this text as their epigraph: Demosthenes, too, assumes that an éranos is not just something to be repaid, but is also a claim on the recipient to do a similar favour another time.
By studying democracy's public institutions, we are prone to underestimate these informal networks among Athenian friends and citizens: the private arbitrations of others' differences and the 'helping whip-rounds' in times of difficulty were important tests of a citizen's temper, already cited by Antiphon in the fifth century and exactly described by Theophrastus, alert to Attic practice and convention. No doubt there the polis' since the time of Hesiod. Since Solon's reforms, rather, Athen had been freed from formal ties of dependence and since 508, nearly two centuries of democracy had helped to entrench a sense of community among Athenian equal rights of citizenship. At Athens, above all, anyone might find hi to arbitrate or to bow to the pressure of an éranos for a friend or fellow-citizen. The Characters' ready references to them encourage us to emphasize otherwise encounter incidentally in Athenian evidence.
In his fine book, Paul Millett has recently studied and emphasized the Characters' allusions to lending and borrowing: in all, the collection has 'almost thirty to credit operations'. They remind us of the distinction between usurers and bankers, that not every lender at interest was a banker and that all sorts of objects be borrowed between friends. This emphasis on 'non-professional' loans is a useful economic reminder, but there are tantalizing hints about attitudes too.
— R. J. Lane Fox: "Theophrastus' "Characters" And The Historian", Proceedings of the Cambridge Philological Society, No. 42, pp.127–170, 1996. (jstor)
The book referenced here is:
Wherever there is a debtor there must also be a creditor, but Comedy naturally stresses the negative side of the relationship. For
a more balanced picture of lending as well as borrowing, there are the Characters of Theophrastus, dating from the final decades of the fourth century. This short text, consisting of thirty brief character sketches or caricatures of people who might be met on the streets of Athens, has almost thirty references to credit operations. The Characters themselves, all of whom are unpleasant or foolish types, repeatedly display their negative qualities by adopting anti-social attitudes towards lending and borrowing.
— Paul C Millet: "Lending and Borrowing in Ancient Athens", Cambridge University Press: Cambridge, New York, 1991, p5. With numerous more elaborations on what can be gleaned from Theophrast, when correlated with other information.