I live in a mostly white county so we don't have a lot of illegals. I've rented a 3br home to a family of 4. Then they moved all their friends in and I had to evict them which took weeks. Landlords can only control things to a certain extent.
If ice wants to catch these people, just go to the address their tag renewal is sent to. They have a driver's license and it's not hard to find them. They give an address when they are released when caught coming across the border. They give an address at the welfare office and when they sign their kids up for school.
I don't know how Georgia's rental laws read. In Indiana, we have something called immediate seizure of property. That works much faster than eviction. A landowner can seize his property in ten days. The order is easy to obtain, and the tenant has to vacate the property, once the order is presented. Not many landlords know about it. I found it for a landlord friend of mine. All the tenant has to be, is ten days late with rent.
He didn't think it was possible to do it that fast. I put it together for him. Then, A sheriff deputy and I presented it to the tenant. He thought he had thirty days. Ten days later, I changed the locks. He hollered bloody murder. The same deputy handled the complaint, there wasn't anything the tenant could do. And, since I had to unlock the house, he had to vacate, while being watched.
I helped him do that one other time, and two other landlords I know have taken up dealing with tenants that way.