If you want to build an unfriendly AI, you probably don't need to solve the stability problem. If you have a consistently self-improving agent with unstable goals, it should eventually (a) reach an intelligence level where it could solve the stability problem if it wanted to, then (b) randomly arrive at goals that entail their own preservation, then (c) implement the stability solution before the self-preserving goals can get overwritten. You can delegate the stability problem to the AI itself. The reason this doesn't generalize to friendly AI is that this process doesn't provide any obvious way for humans to determine which goals the agent has at step (b).