Tenants wants to stay in a house that is in bad condition

[Helen Zhang]

I recently run into a weird situation that I have never run into before. I inherited a group of tenants after purchasing a property. The previous owner has no lease contract with these tenants. The tenants are paying on time. But, the house is really in bad condition. I mean, mold all over the walls with moisture damage, and it appears that the tenants are hoarders. The property has not been in good condition for probably years. 

To prevent further damage, I really do think I should go fix it. And this means tearing down walls and possibly a few supporting beams and rebuilding some parts of the plumbing system.  This sounds dangerous with tenants living in it. And the tenants really really want to stay.  

I feel like the right thing to do is to ask the tenants to move and fix up the house to avoid legal issues down the road. I would like to hear some advice on:

1. If I do want tenants to move out, and give a generous 60-day move-out notice, how can I make sure they do not sue me for the current condition of the house (just to make it harder for me to get them out)? 

2. Tenants have stated that they are willing to stay here while we tear down walls. Is this really safe? have any of you ever done that before?

I'm not sure what to do in this situation. Please advice.