Your identity is not tied to your instance. If your instance closes up shop, you keep all your followers, followees, DMs, etc
This is one of the major advantages Bluesky’s protocol (AT Protocol) has over ActivityPub. ActivityPub doesn’t have anything built-in to support this. On Bluesky, you can use your own domain name as your username, and freely move from one server to another while keeping the same username (once they open up federation). It’s configured through a DNS TXT record.