That's pretty hilarious actually. In any game, it's always more comforting to have a safe house. And I've never so far run into a situation where my players actually kill someone to take their place. In a city or village, if they kill the owner, the neighbor will alert the guards as soon as they notice his disappearance (that could turn into a cool CSI-type court ordeal where the players have detectives on their tail that keep removing their sunglasses, damn them.... yeeeeeeeeeahh). I don't even think it's legal to kill a hobo. (That's why most GM discourage the neutral alignment, if 2 players are good, they'll be opposed to it.)
The problem with a cave is that any other creature (or adventurers) might walk in there, which again, might make for some ordeal where the players chase after a thief (which is just a legitimate adventurer who found shit laying around).
I've always had a Base of Operations for my players in my game, simply because they usually belong to some group or guild. Even when I run a more survival horror game, they have a place they consider less dangerous although it most likely will get torn down at some point. If I ran a game where the players traveled the world, I'd give them the option to buy a house or establishment in any city they like. Considering the economy in D&D is so fucked up that most of the world's gold is held my monsters, it wouldn't even be so hard to buy. If they want to buy the WHOLE town, now that could be even more interesting and something they'd have to work at but I'd still let them. People are suckers for gold.