MX record change and you’re off to the races. Tangentially, I’d also be interested in putting an acquisition together to acquire FastMail if ever in financial peril, in order for it to persist as a going concern and arguably, a public good (like Let’s Encrypt).

If you own your domain and make regular data exports/backups, nothing.

If you use it with domain you own, you can just point it to another email provider.

What happens when Google kills Gmail?

That's my point.