With today's eviction rules ... no way would I allow anyone to stay in a house I just purchased!
When I bought my first house back in 2016 it was occupied as a rental. I was in an apartment lease for another 9 months (could afford both anyway) so it worked in everyone's favor to get the closing pushed back.
However, at the last minute - as in the day before final walkthrough / closing - the tennants sprung it on the sellers that they were under the impression they going to rent from me. I got a frantic call from the my realtor at the last minute ... news to me! I have never spoke to the people.
I don't know the people who were living there, but I'm not a gambling man so I said NO to that. Either we delay closing or they get the tenants out. I kinda felt bad, but they were made well aware of the house getting sold.
They moved out and left a lot of stuff behind. Turns out they were not good people. I'm glad I didn't decide to rent to them. Who knows how that would have went.