During a Gallic revolution against Rome, a Gallic army of some 80,000 men took shelter in the fortress town of Alesia, where they were besieged by some 50,000 Romans under Julius Caesar. (His army may also have included some non-combatants such as builders, wagon drivers, etc. that brought the total to 60,000 or 70,000.) Thus the Roman army was numerically inferior but qualitatively superior, having beaten the Gauls in a pitched battle at Gergovia.
Vercingetorix managed to send some cavalry through the Roman lines to seek help, (which was forthcoming), but otherwise did little to arrest the progress of the siege. Because of that fact, the Romans were able to complete a line of "circumvallation" fortifications between their lines and Alesia, and then another set of lines of "contravallation" between the OUTSIDE of their armies and the relieving forces.
One line of defense against the "mining" of a besieged city is "countermining." In this case, it would have consisted of constructing one or more trenches from Alesia perpendicular to the "circumvallation" fortifications. This would have allowed the Gauls to approach the Roman lines for hand-to-hand combat under the protection of their own trenches.
Would it have made sense for the Gauls to engage in an all-out war of attrition to disrupt the circumvallation process? They were no match for the Romans in open field, but might they have been more successful in a confined area, particularly in say, night attacks?
The purpose would NOT to break out, but to weaken the Romans vis a vis the relieving Gallic forces (of over 100,000), perhaps by trading casualties at a 2 to 1 ratio (40,000 Gauls for 20,000 Romans). And if they could set back the Romans' timetable so they could build only the inner wall but not the outer wall, might it have been worth it?
Given that the besieged Gauls were short of food other implications were 1) battlefield casualties would have meant fewer mouths to feed, and 2) the opportunity to capture some supplies from the Romans (most soldiers carried some of their own food).
Or was Vercingetorix's "better" option to wait for a battle on the "last day" before his besieged army ran out of food (as he did), even though he lost?