[AgentME]

The cost of mining doesn't set a price floor. If the price of Bitcoin falls so that the revenue of mining falls below the costs of mining, then miners will drop out until the cost of mining falls enough too.

Bitcoin is minted at a predefined global rate; the amount minted doesn't depend on the number of miners. Miners compete with each other for a share of the predefined minting action, so some dropping out does not decrease the minting rate of Bitcoin, but instead makes it more profitable for the remaining miners.

[mywittyname]

It does set a price floor for exactly the reasons you say: miners won't operate below a certain cost of mining. Setting a price floor.

[AgentME]

If Bitcoin's price fell so it becomes unprofitable to mine, that will not cause Bitcoin's price to go up until it is profitable for miners. Instead, what will happen is that miners will drop out until mining becomes profitable for the remaining miners.