If they stopped producing more of any currency it would cause hyper deflation, as worker productivity increases all the time. The gold price would also skyrocket if they stopped mining gold.
You misunderstood something there.
The mining process works like this and it's ALWAYS the same!!! No matter if the Bitcoin price rises/drops. My explanation:
-The mining network mines blocks and obtains the block reward of this block.
-Currently, the Block Reward of 1 block is 12.50 Bitcoins. At the beginning it was 4 times as much: 50 Bitcoins. Once every 210,000 Blocks have been mined, the reward per Block (in BTC) halves.
-Each Block is mined in approximately 10 minutes. When it takes shorter than 10 minutes, the difficulty will adjust itself to become a bit higher, so all blocks will be mined in approximately 10 minutes.
Now let's get to your thing:
-Price goes up
-More people start mining, because Bitcoin became worth more, which makes the Bitcoin block reward higher, so the mining rate increases.
-Mining rate increases, so the next block will be mined in a bit less than 10 minutes, but the system will adjust itself, so the next blocks will be mined in exactly 10 minutes again.
-Therefore, the rate at which new coins are added to circulation stays the same.
I hope this helped!