Aaccept new tenant while house is selling?

[Jack B.]

So I had a buyer and his financing allegedly fell through. Left me holding two vacant units I gave that I gave notice to and moved on before deal fell apart, now thanks to novice buyer I'm left holding the bag.

I have a new buyer but also a new prospective tenant ready to move in Saturday. If sale goes through the tenant would have to move out by end of March. Notice would need to be given a week after moving in.

If the sale falls apart and I let this tenant slip away under assumption that deal will close I'll really be mad. On the other hand, the appraisal will occur after they move into the apartment just days before I'd have to give notice anyway. Should I just cancel the holding deposit for tenant and risk more vacancy if sale falls through again or move forward with them just in case?