Palimony is the idea that if a
couple live in what is essentially a traditional
marriage without an actual ceremony, then a
partner is entitled to the same
alimony for support in the event of a
breakup as a married woman would have been after a
divorce. If two people
explicitly or
implicitly form a
joint effort to accumulate
property, then that property is to be divided fairly after the breakup of that relationship.
The most famous case to use this concept was that of Michelle Triola (aka Michelle Marvin) against actor Lee Marvin in 1976; the two had made an oral agreement that while "the parties lived together they would combine their efforts and earnings and would share equally any and all property accumulated as a result of their efforts whether individual or combined." In other words, they had promised to split everything, and Michelle would "render her services as a companion, homemaker, housekeeper and cook."
When the two broke up and Lee Marvin didn't want to divide their property equally, it went to court, and the first judge ruled that this contract was unenforceable. On appeal, the California Supreme Court reversed the decision, saying that "a contract between nonmarital partners is unenforceable only to the extent that it explicitly rests upon the immoral and illicit consideration of meretricious sexual services." Though this case rested on there having been an explicit agreement between the two, the California Supreme Court went on to emphasize "the property rights of a nonmarital partner in the absence of an express contract."
Just as not all women in divorce cases receive alimony, not all breakups of nonmarital relationships qualify for palimony -- there has to have been at least an implied agreement that the two were working as a team who would share things they acquired.