What happens to gift bushes when they are not redeemed by the player that received them?

What happens when a player receives a gifted bush and doesn't dig it up in exchange for diamonds or coins?

Nothing that I'm aware of. Players can leave gifted bushes on their island as long as they desire.

They can't be moved by the recipient, but they don't expire. Many players leave them on their island for months (or years). It's their right to do so.

If the player who receives bushes logs in, the bush will just sit there until they remove it. If the player does not log in, the bushes will not appear on their island. It just will be gone in cyberspace.