There are lots of Solo miners who will be very happy if major mining farms take a break just even an hour due to the fall in the price of Bitcoin, so with regards to the question of do miners drop when the price of Bitcoin drops, then I will say they don't, because considering how much these miners generate after mining each block, it's enough to cover any loses caused by a recent price drop. However, I just checked the recent block mining, and all I could see are still the major Bitcoin miners, which is a clear sign that no miners left due to the fall in price of Bitcoin. Example, miners such as AntPool, SpiderPool, F2Pool, and Foundry USA Pool., which have been known to consistently mining the recent Bitcoin blocks.
In the long run, the expected profit of both solo mining and pool mining will actually be the same. If big miners are willing to scale down their operations, you're likely screwed over as a small miner or a solo miner already. If you're a small miner, you're likely to join a pool to ensure that your payouts are regular and consistent. I isn't likely that any of the bigger miners will shut off their equipment just because the price has dropped.
For most solo miners, they're usually into lottery mining which is not affected by the price of Bitcoin. Their decisions made should largely be independent of the price fluctuation.