How can a server recover from its secret key stolen?

Question

Suppose a server use digital signature to prove the files it sends to users. If someone steals the secret key in the server, what should it do?

Answer 1

The key needs to be revoked, the server nuked from orbit, and a new system with a new key put into place.

To go further, this is why you want your master signing key to be offline and trust in your servers' certs based on that chain.