The Collaborative International Dictionary of English v.0.48:

palimony \pal"i*mo`ny\ (p[a^]l"[i^]*m[=o]`n[y^]), n. [pal +
   alimony. (ca. 1975)]
   a form of alimony paid to a former partner in a romantic
   relationship after a period of living together, even though
   the two persons involved were not married to each other. The
   absence of a formal marriage distinguishes it from alimony.
   [PJC]

WordNet (r) 3.0 (2006):

palimony
    n 1: support paid by one half of an unmarried partnership after
         the relationship ends