Mastodon servers may eventually close down, but the well-run reliable ones will give you three months warning if this is happening. This gives you time to transfer your account to another server.
More info about server shutdowns in the guide at:
➡️ https://fedi.tips/what-if-a-server-closes-down-what-happens-to-my-account
The guide also answers lots of questions about this topic. Please ask in the replies if your question isn't answered in the guide 🙂
