Even the fastest, most dumb FIX gateways need to maintain order state, because exchange can send (via FIX) partial fills and acks, and customer can send (via other MOM) cancels and amends, in full-duplex.
When an order is completed, it should be removed from memory to free up. Before that, the engine needs to maintain its state. State maintenance is a major cost and burden on a low-latency system.
A sell-side FIX engine is a daemon process waiting for Response from liquidity venue, and mkt/limit orders from buy-side clients.
[[Complete guide to capital markets]] has some brief coverage on OMS and state maintenance.