I think it would be more appropriate to ask "what were the social statuses of men who failed the civil service exams?
For this I would point you to the Wikipedia article on Imperial Civil Service Exams
Even though only a small fraction (about 5 percent) of those who
attempted the examinations actually passed them and even fewer
received titles, the hope of eventual success sustained their
commitment. Those who failed to pass did not lose wealth or local
social standing; as dedicated believers in Confucian orthodoxy, they
served, without the benefit of state appointments, as teachers,
patrons of the arts, and managers of local projects, such as
irrigation works, schools, or charitable foundations.
It seems as though, especially in your area of interest roughly the Yuan Dynasty to the Qing Dynasty, failure of the exams was not viewed with particular disdain. Rather, while failure was obviously not as prestigious as passing the exams, the fact that one had sat for the exams at all was a powerful indicator of relative social standing. Often, study periods for the exams would last several years and consume much of the waking hours of an exam candidate. The very fact that one had been able to afford and then undertake such an expensive and time-consuming endeavor points to relative wealth, intelligence and perseverance.
Through some correspondence with an acquaintance of mine who specializes in Chinese and Tibetan History, I stand by the answer above with one small caveat. Although the exams were difficult to pass the amount of money, time and effort invested in them meant that failure could be a huge loss of face. Many examinees were crushed and became bitter and disenfranchised.
Note also that there were multiple levels of the exams. Think of them as the local or municipal level, provincial level and nation wide level exams. It was statistically much easier to pass the local level exams than the imperial level exams and getting a local certification could make you the local big man on campus.