Borders don't exist. They are figment of the Hominoid's imagination. A pseudo social science experiment, nothing more. Did dinosaurs have passports? Will the cockroaches and beetles require a VISA to cross over an imaginary line after humans have wiped themselves out?
No, they will move from place to place freely in search of food, shelter and a better life for their babies. It's no different from what human migrants are doing now and have done for thousands of years. We are all animals, the only thing that separates us from our insect ancestors is consciousness, a tragic misstep in evolution IMO.