Once a remote server has no more cards in it but the ice that protected it remains, what happens to it? Can I put more cards into it later, and the ice protects them instead?

Venthrac said:

Yes. As long as there is either ice, and/or an upgrade/asset/agenda installed, a server will persist. Once there are no cards both in and protecting the server, it automatically disappears.

Kinda like cloud-based computing.

Great, thanks!

This makes it really nice to build up a secure data fort or two, and your effort of rezzing IC doesn't go to waste. Remember, you can create a datafort without the play of an agenda or asset, simply installing IC will suffice. This means you can get a nice cozy home for agendas and assets, before exposing them to harm (of course, your hand is always a viable target!).

You can install ICE on central data forts (HQ, R&D and Archives), too. The only difference is that these exist even when empty and unprotected (Archives starts out that way).