Responses
http://www.mangago.me/read-manga/shitsukekata_nijuumaru/
I don't think this is the one u r looking for but it somewhat matches ur criteria.
Oh thnks!
Any yaois where the character was either found to have given up i.e sitting at the dumpster or trying to end his life by the other chara and was taken in to be their ( sex ) pet / slave instead?