What can I do if a Tenant leaves all of their belongings behind after an eviction and a writ of possession has been enforced?

What can I do if a Tenant leaves all of their belongings behind after an eviction and a writ of posession has been enforced?
Handle belongings in accordance with the "abandoned personal property" rules of your state's L-T law.

At least here TN, if an official court eviction happens, the sheriff office sends a officer out to stand there while you move everything to the curb. This is also how they do it in GA. But you will have to check the laws in your state

If you have someplace where you can store them, I would do so for a month and if they are unclaimed, have a yard sale or donate them to charity.