Of course we can compare any cases with current situation at criprocurrency market. However, it seems to me that BTC cap will be increased in several times at least and considering mining costs for 1 BTC (more than 1k $) the BTC price can not be less than 1-1.5 k $
This is precisely where you are wrong. When the price of BTC falls below the cost to mine, miners will simply stop their operations. This means that anyone having Bitcoin will not be able to sell them or do anything with them. This in reality will mean their value becomes zero when you are not able to sell or buy at all.