I'm thinking of playing as a homeless sim starting with nothing at all and I was wondering if it's at all possible to not buy a lot for my sim, so that they're truly homeless. Does the game even allow you to do that? If not, is there a mod that removes the requirement for a household to be tied to a specific lot in the world?

I don't think so. Paralives does that, but TS3, I can't imagine how.

I always just buy an empty lot, cheat my household money to zero with Master Controller and then proceed to ignore it by sleeping on benches and wash at the sink in a public bathroom. I have a mod that charges for the gym, so that's not an option to shower for free. Sometimes, I use the junkyard to start furnishing my empty lot and make it look like a homeless encampment, if I develop the handy skill.

https://modthesims.info/d/522749/up...ade-usable.html

Thanks for the suggestion! By the way, if I may ask, what mod do you use to make gym showering not free,?

I think Devil's Port is the Bridgeport alternate I have... https://shulzfinds.tumblr.com/post/...rt-need-all-eps
There is actually a homeless camp under a bridge.