Has anyone ever heard of an op amp oscillating after it saturates?
I have seen this in an op-amp designed to go to the rail. It oscillated continuously with a very small amplitude when the output was very near the negative rail (tens of mV). Probably the frequency compensation was ineffective in this range. 

Quite a few years ago, so I don't remember the details, but I think it was an LMV324 type. 

Ended up not using the part that behaved that way.