Membership and Directory, remove a listing

I've failed at trying to integrate Sabai-Directory and Appointments+ so now I'm going to take a crack at it with WPMU Dev's Directory plugin.

How can I automate the removal of listings?
Directory only uses payments to grant the ability to create listings.

With Membership I can stop someone from making new listings as well or from viewing them.

What I need is if someone is no longer paying for a certain 'Membership' level. Their listings are removed automatically, either immediately or after a week or so. Is this possible and if so, how?