Option A:  It can solve it the same way we do security in meatspace: rent itself a facility and hire armed guards to keep thieves out.

Option B:  A distributed algorithm to generate keys might be possible.  Sort of like a multi-party PKI variant of  Diffie-Hellman key exchange, resulting in all parties knowing the public key, but the secret key is only recoverable when all nodes agree it's time to perform a spend.  I wonder if anyone has created such an algorithm.