So, rather than banning them, move them to a new group called "Inactive", and strip out the rights to do much of anything on your site. You can then make a block in Pages or a notice that only shows to that group that their membership has expired. If you're using Commerce, you can have your membership packages in there and direct them to it for payment, and Commerce will automagically bump them back to the membership level you specify.
Using Commerce, this whole process can be automatic. When they expire, it will bump them down to Inactive and when they pay, it will bump them back up. You can manually process this too for your old memberships that you're carrying over.