Well, he may have a child. Well, clearly that seems to be implied. I mean, he is the 'Godfather' of the Robot Mafia. So if he is a parody of a Mafia boss, he will most certainly care about his family.
Well, I had this idea with no support whatsoever (except for maybe that scene, and the episode "Bender Gets Made"), but knowing the nature of Futurama with such twists like Fry's purpose, Leela's parents, and Farnsworth's son, well, I kind of get this "hunch" that Tinny Tim may be (or become, they may have just came up with this concept) the son of Donbot and Fanny. He did live in little Bitaly, a place that's destined to have a mafia. Maybe Tinny Tim isn't as pitiful as the writers make him out to be- he has a crutch for an arm and a crippled leg possibly just because he was built that way. He may be going home to someplace nice (or, if my theory's false, then he wouldn't be going home at all).