I manage properties and have had some clients that have bought occupied units or I have taken over for their previous managers. First check your local laws. Here in Missouri I have to honor an existing lease unless I can get the tenant to agree to my terms and have them sign my lease. If they do sign my lease, usually don't extend it past the period their lease would have been. I want to know they are good tenants before I lock them into a longer lease. Second, ask he seller for the rent ledger to make sure the tenants are paying on time. Lastly, and possibly the most important, make sure the security deposits are transferred to you at the sale. I know in Missouri, deposits are supposed to be held in a separate account.Technically that is not the seller's money, it is the tenant's and you don't want to be responsible for money you never had in your possession. If I know my client never got the deposit I tell the tenant as soon as possible so they can contact the person they paid their deposit to.