When a rental becomes 'vacant', you can move the Tenant File an 'Inactive File'. There, the Tenant can still be maintained, and transactions (such as back rent owed) can be posted. In fact, you can run many of the Tenant File reports in the Inactive File.

When you are finished working with the Inactive File, it is easy to switch back to the 'Active File' and continue working. 

Even though you move a Tenant to the Inactive File, the transactions that pertain to the Owner are preserved in the Owner's accounting.