If someone or something is on a slippery slope, it's in a situation which is getting worse and will continue to get much worse. Sometimes we say it's 'going downhill'.
如果说某人或某事 on a slippery slope ，就是说处境糟糕，而且会更糟。
Examples:
The country's economy was on a slippery slope following the closure of its biggest industry.
With his big drinking problem he was on a slippery slope to bad health.
