This answer only deals with the Late Imperial period (Ming and mostly Qing), which is the period we have the most data on and thus the most scholarship. It also mostly ignores regional variations.

-Yes, there were a lot of men who never married. This was in part, as you point out, because of sex-selective infanticide, in part because a tiny handful of men had more than one woman. (Which could mean the official wife, (qi 妻) any concubines, (qie 妾) and whatever maidservants were in the household (bi 婢) This created all sorts of problems both for the men in the status of “bare sticks” (guanggun 光棍) and for society as a whole. Members of the elite wrote a lot about the problem of bare sticks, who lacked money and family and were ripe for becoming bandits or salt smugglers or other kinds of troublemakers. Bare sticks were, by definition, poor. They lacked the money to buy a woman, or the resources to make her financially secure if they did get one. Sommer points out that the dividing line between paying the bride price for a wife and buying a concubine was legally clear, but in practice not all that important. Women’s bodies were a commodity, and these guys lacked the money (and property and social status) to acquire one.

The radical feminist He-Yin Zhen described the situation in a 1907 essay

In the homes of high officials or large extended families, the number of concubines can reach more than ten. [In contrast,] in such places as Yancheng, Xinghua, and Gaoyou counties [in Jiangsu], among the lower classes one woman belongs to many men; or younger and older brothers share a wife. In Yangzhou, peasants who have many sons always provide a wife for the eldest, whereas the sons next in line can never marry.... [A] country with a system of one man and many wives has to have a system of one woman and many husbands. Moreover, there have to be a certain number of men who have no wives, and those without wives are sure to be the poor. the evil of the wealthy lies not only in raping the daughters of the poor, but also in tacitly stealing the wives of poor men (Sommer pg 53)

What do men want women for, and what do women want men for? Sex is one, but also production of heirs, doing women’s work, financial security etc. Affection may fit in here as well, but since a lot of the evidence we have is from court cases we don’t see much of that. There were any number of strategies for poor men (and their families) to get a woman. Some of these were legal, some not, some more or less socially respectable.

-#1 the minor form of marriage or adopting a daughter in law. (tongyangxi童养媳) This involved adopting in a young girl who would be raised in the family of her future husband and then, once she was grown, told that she was now the wife of the guy who had been more or less her brother. This saved the family the bride price and also it was not considered necessary to have a big wedding (a major expense.) Although this saved money and could be found in most places in China and was quite common in some, it was seen as a desperate move by a poor family. Adopted in daughters in law were proverbially unhappy, and the marriages that resulted usually miserable. On the other hand it was completely legal

-There were also various ways for more than one man to share a wife.

-#2 was a simple wife sale, where in exchange for cash or other considerations a woman would go from being the wife of one man to the wife (or concubine) of another. This was a violation of Confucian ethics, since a woman was only supposed to have one husband in her lifetime, although that was more a concern for the elite. Still, while this was legal, it was socially tricky. In theory the decision to sell a wife was the husband’s, at least in the Ming, and he could do it without a matchmaker or approval of her natal family. He could sell her even if she had fulfilled her duty of having sons to carry on the family line, and in theory she could not push for a sale if she was unhappy with his poverty or otherwise wanted a new husband. In practice, none of those things were necessarily true. (see Sommer chapter four) Usually the wife and the natal family and a matchmaker all had to approve of the transaction. One of the points Sommer makes is that this (and “getting a husband to support a husband” below) were things that the wife had to accept or at least acquiesce to. Methods #2 and #3 were socially questionable or outright illegal, and if the woman was not willing to tolerate the switch she could gum things up.

-#3 “Getting a husband to support a husband” (zhao fu yang fu 招夫养夫) This involved bringing in a second man to sleep with and usually live with a married couple. This was illegal, but apparently happened pretty often, and there were often formal contracts for it. Although socially highly dubious, it was accepted in some cases as the only way for a family (often with some sort of sick husband) to stay together. Ideally the incoming man could work and bring in money, and he would get sex and other womanly services (sewing, cooking etc.) and usually live with the family. There might be some sort of agreement about which family any later sons would be assumed to be from. As I said, this was illegal, and also something that the family of the couple would regard as highly disreputable.

So there were strategies for men too poor to marry in the ordinary way to get a woman. These seem to have been pretty common in the sense that they happened all over China, and law codes and elite writers seemed to be quite familiar with the strategies. Most of what we know about this comes from legal cases, and there are probably lots of cases where these things happened and there was -not- a breach of contract or a jealous murder and thus we know nothing about them. So it is not clear how common these sorts of arrangements were.

Source

Sommer, Matthew. Polyandry and Wife-Selling in Qing Dynasty China: Survival Strategies and Judicial Interventions. Oakland, California: University of California Press, 2015.

There is a big literature on all this, but Sommer is really good and summarizes all of the earlier stuff