I guess I'm thinking of two things...but the one that is related to animals is this. I have 2 kittens right now....that belong to one of my cats. I love them and play with them and treat them as my own but deep in my heart, I know that they are destined to have new homes...I can't keep them here. I know I'll cry when they go, but it won't be the same as if someone were to come and take one of MY cats. Make sense?
I know the program Susan is talking about and I think it's a very worthwhile effort if you have the heart and patience for it. If it weren't for others socializing the pups and kittens, I fear their placement options would be severely limited. Some folks that are foster parents for pets have children so the new animal learns to be around people and children. Others don't have children, but have other animals that the foster pet can learn to be around.
I think I would be more concerned about how well my own pets would cope with a new friend and then the absence of the new friend. We had 2 labs in the house at one time. One of them died over the summer...the other is still very clingy and mopey...she misses her friend and grieves for him (okay....me too). I'd hate to purposely do that to one of my critters...hence, I do not take part in the foster care animal program at this time.