Abandoning a pet and re-homing are two very different things.
I dont understand the mentality of getting rid of a pet (because its easier) and then replacing it once your moved into a new place with another one. I mean really???? You have a bond with that pet and a responsibility to that pet (any animal you bring into your home) and to me there IS NO EXCUSE to leave an animal behind in an empty building left to fend for itself until some unexpecting person comes along (hopefully before its too late) and steps in to do the right thing.
To me a pet is the same thing as a child. They are unable to care for themselves. Ultimately you are responsible, no excuses. In my life I have had to move, I have lost a job and have gone through a divorce all without abandoning my pets.