You joke, and Gosford is an unfair example considering that they never really had a team, and nobody would probably miss them if they did, but it happens.
Let's take one example; Houston in the NFL.
Through the 90s the Houston Oilers owner, Bud Adams, lobbied Houston for a new stadium. They wouldn't give it to him, so he moved the team to Tennessee in 1997 and renamed them the Titans.
Houston, and Texas in general, is a huge and important market for the NFL, so they and the owners group only approved the Oilers move because there was no mending the bridge between Adams and the local government in Houston, and then fast tracked expansion so that they could replace the Oilers as quickly as possible. The Houston Texans were founded in 99 and joined the league in 02.
There're plenty of other examples as well, and not just from the NFL.