I don't know any fics where the captive/pet kills himself to escape, but Sam wishes he could die before inevitably breaking like Cas did when Demon!Dean has him and Castiel as his pets and it gets pretty dark treatment in most of the fics in the Rainbow Marble Series by PetrichorPerfume on AO3: http://archiveofourown.org/series/116182

Dean/Death pairing isn't my thing but otp_destiel on livejournal wrote Little Deaths and At Death's Door: http://otp-destiel.livejournal.com/50152.html