When ETH goes entirely to POS, it will be the end of ETH, or at least they will face many problems. POS consensus mechanism is not as reliable as POW. But I would like that to happen so that we can finally see how POS works in a practical environment which is competitive enough to pose challenges to the algo. The weaknesses of POS will be come visible very soon after the shift. As for the miners, the miners will switch to another coin, or several coins which they think are the most profitable. ETC may be among those coins.
I would like to see this scenario actually. Personally,,, I am not sure how much we can trust POS but to be fair we have not seen it being in full implementation with a big platform with lots of transactions so perhaps let us give ETH a chance. It does seem to be doing well so far. If they switch to ETC it will be a strange case. Will ETC run into the same problems as ETH afterwards?
As far as I know, the ETC is not the ETH's official fork, and each has separate teams. And when we think like that, they do not need to continue from the same way. I am not knowledgeable about mining a lot, just tried to use logic. 
You really need to go back to basics and learn about ETC and ETH. You got it completely wrong.