I have a very close friend who is going to come live with me. Will it affect my SSI?

You are a good friend and are risking that friendship by opening your home. Any relationship is difficult at times. Do yourself and your friend a huge favor and discuss the minutia as even the smallest thing can blow up when the bloom is off the rose. Regardless of the SSI issues you would be very foolish to think things won't go wrong at times. Are you now a landlord? A co-tenant? Be careful that you don't create a problem for down the road. You say "they" so is this a couple? What happens if one of them passes? Are you now the caretaker of the other? I'm not suggesting you don't help your friend, I'm just imagining what could happen. I hope it's all blue sky and you enjoy having others in your space.

Possumlvr, this is what Medicare has to say about your question.

https://www.medicare.gov/coverage/home-health-services.html

Does medicare cover care givers? I'm on social security disability and I need help. Someone told me they think they did but I don't think so.

You should both be OK. Just get a written agreement to share costs 50-50.