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?
As pointed out its year 2040 or 2041. Even the last bitcoin mined is unpredictable AFAIK. Its really depends on how the blocks is mined (every 10 minutes?).
I think there's going to be a Asics or mining hardware in the future that will be "eco-friendly", that will not consumed so much hash power. Oh yes, solar panel will be a good alternative as well.
As for the software, not sure though it we need to augment. It doesn't really makes sense.