To be on the slippery slope

To be on the slippery slope:
Syn: to be on the wrong track, to go downhill 

• The country's economy was on a slippery slope following the closure of its biggest industry. - être sur la mauvaise pente

•  With his big drinking problem he was on a slippery slope to bad health.

To go downhill

• The company went downhill after it lost its best contract.- dégringoler, décliner

As slippery as an eel
it means they are not honest and you can't trust them. It is difficult to catch them behaving in this way.