To answer the question, as density altitude increases stall margin decreases.
The early P&W JT9-3A engines had a throttle bar - a simple sliding blocker - slid into place when operating above F290 to prevent closing the thrust levers all the way. Sometimes when the gas path was a bit buggered up they would simply surge in cruise when the air density changed by flying into a different parcel of air. Kept the FEs awake!! You did, however, become very adept at running the engine failure checklist followed by the inflight start checklist. With luck you could get a relight without needing to descend.