If a server were to be shutdown(lack of financing or any other reason) would all the content posted there be lost too?
Is there anything the admins do or can do to prevent this? Any Mastodon instance featured on the main webpage for example offers a guarantee to at least warn users months before the shutdown.
Could the content be perhaps moved to another server like mastodon people can move over their followers?
Yep.
Content always has two links, the “federated link”, IE the official version, and a local link.
In the case of that server going down, the federated link wouldn’t work, but the local one would.