I recommend an option in admin panel for Enable/Disable remove listings by users.

Because, They usually prefer to remove their old free listings and add new ones.

Their new listings go to top of list and they do not need to buy featured or BumpUp/Highlight for their old free listings.

We can install listing status plugin and add new status for the listings, like hidden, Sold, Sold Out,...

So users can change status of ads, instead of removing them.

Removing ads should be done only by admin in admin panel or running cron job.