So it is year 2024 and the max BTC supply is reached at ~21M.
I'll speculate that the price of energy around the world will be higher than it is today, so that will cut into the miners profits. They will also be receiving their BTC on fees alone, not the generation of BTC for completing the block (like today).
Will it be economical to continue mining BTC going forward? The large mining operations can always set up a solar panel system to reduce energy costs.
Even if some of the larger miners shut down, I'm sure there will be enough miners around the world where the blocks will still be completed, but it may take longer. (The mempool may grow like it did before X-mas last year) I'm not exactly sure how the lightning network will affect the mempool....?
Is it possible that the S/W for BTC may be augmented to a semi POS type of system?
Maybe its possible but it take years though , but nobody can say , if you mine all that then the blocks gonna be zero and theres nothing left to mine. Its up to you how you can do it , but I think it would be possible though but it takes time and its worth it really worth it.