Is it weird to ask a stranger to live with you for a bit?

YES IT IS WEIRD BECAUSE YOU DON'T KNOW THE PERSON. THEY CAN BE A CRIMINAL,

A RAPIST OR SOMETHING BAD.

That's a novel idea. It just might work. Thinking of the down side:

!.) You may be tempted to use the live-in as a therapist and talk about your break up. She has no qualifications to really help you other than give a second opinion. Moreover, you may talk obsessively about your break up and that will cause you more harm than good.

2.) You said that it is a small town. People will talk. For sure.

3.) You may become sexually intimate with the live-in as a quick fix. That's not going to do you or her any good.

Sounds to me that you need a friend to talk to. Everyone eventually gets tired (sooner rather than later) of listening to a sad sack friend constantly moaning and crying about a lost love. Buck up and move on. Easier said than done. I know. Try finding new interests or get re-involved in old interests ... hobbies, sports, pastimes, etc. Make new friends.

Don't stew or obsess in your broken heart.

I never heard of such a thing but this is quite interesting. I think its a good idea. As a human being, we all need that human interaction and such.

its better u get kno the person first n their background n be friend them