I started rescuing before "fostering" was a thing. I did it on my own - if I couldn't find a home, the animal was mine. There were some that I was very happy to find a home for. :)
One thing I always did was to offer free babysitting when the new owners needed. It allowed me to see how the animal was doing. The best part was that when they brought the dog over, it would be "oh OK I guess that was just temporary. OK I'll live here again".
When the owners came to get the dog, it would do a Sally Field "you like me! You really really like me!"
The owners would call me a few days later to say how much more attached the dog was to them - it just seems to really let the dog know it has a real home and its own people.