Strategies to address an immutable key in a symmetric cryptosystem
I'm not sure if this is precisely what you are asking, but developing single-session keys from a long term hard-wired key is something that mobile phones and SIM cards do. Hard-wired keys on the SIM and known to the service provider kick off key derivation process augmented with a random nonce value from the service provider's base station. The 3GPP MILENAGE suite is such a method, is standardised via ETSI, and only uses symmetric primitives (block ciphers).