I have contemplating about this and even consider capturing data however havent had a chance yet.
I presume if the coin price plummets then people will lose interest and move to other profitable coin and as a result, falling coin's difficulty would decrease but so far I havent quite noticed that with zcash. Sometimes it seems opposite is happening.
But I'd really need to capture long term data over long enough time range to see any relationship and/or pattern being observed.
For the basics, people will mine the most profitable coin they could see at any online calculators. then difficulty of that coin will rise, however, it is more profitable to mine a decent coin like zcash as even though the price has plummeted it still can increase long terms. it is a mine and Hold strategy. another thing is that zcash can be mined on old GPU's like AMD280's.