I gave my first BOs a notice and just double paid board so there was nothing they could do. They knew I was leaving and the most I got was a dirty look. They weren't going to treat my horse any differently because they were animal lovers, they are just the type of people that will do anything for money (always asking for donations and volunteers and offering all kinds of random services to make a buck), so when one of their only 3 boarded horses was leaving, they were losing a bit of money.
I work at my current barn at least 3 days a week and am there all the time, so I know all of the horses well. We've had people come and go. Rarely does someone leave because of us. In fact, I can only think of a couple of people who have left in the last year. One on perfectly good terms and is still a friend of the owners. She just had a better trainer opportunity elsewhere. The other was not perfect. The BOs are very nice and accepted her lie as truth because she had mentioned her situation a few times. It was a white lie and she never paid her 30 day notice.
The only other people who have left have been asked to leave. We never treated their horses differently before they left...mostly because we were glad they were leaving. Why leave them on even worse terms than they already are?