Not by the EA standard way of moving to a new town, the old one will be destroyed. But with NRaas Traveler, you can move to a new town, while keeping the old one intact. Head on over to the NRaas website, and read through the FAQ for the Traveler mod, it will have all the information you need on how to do this.
I have moved my family of over 30 generations many times. I save the current town. I put a copy of them in the library. I place them in the new town. I do a new save there. I have all the saves or darn all from all the places they have lived in the past. When I need to go back for any reason those saves are intact.