I don't think that they will go out of business as well, they have ample time to adjust to the next mining model in ETH 2.0 so I'm sure majority of them are going to move as well with 32 ETH staking. And besides, if minority opted not to mine ETH then they have other options as well. It's not a death cross for miners, and I'm sure that if there are big incentives moving to POS functioning network, then they will do it, same as to what we have seen in bitcoin hash-rate post halving.
About miners going out of business is something we can't talk about presently, I don't know if POW will be erased entirely from ethereum blockchain, I've seen coins that has both POW and POS functioning on same network, all we can do is wait and see.