It's 2040, the last bitcoin was just mined...

[cryptoJJJ]

Last bitcoin will be mined in 2140 not 2040, after this point the miners will have to live from the transactions fees, and they will most likely also live from bitcoin side blockchains.

[KingScorpio]

What might the miners do at this junction?

Sure, they still get transaction fees. Would those escalate?

Might there be a reason to move to non-ASIC hardware?

Or a reason to change the reward algorithm?

there could be proposal to redistribute old lost coins, like any coins stuck for 120 years ( more then average life span of human ) in a wallet should be redistributed as block reward

and what if someone wants to bury a treasure for his future family member after 120 or more years?

you steal his "bitcoin" and limit therefore freedom over his property

[karsy]

It will be in 2140. I think before this date the reward system will be updated. Bitcoin should cost very high so it would be profitable for miners to stay in bitcoin and process transactions with their ASIC miners.

[squatter]

Miners will have to adapt and earn from fees, and if BTC becomes a globally accepted payment instrument then number of transaction will increase, which will make a stable profit for miners.

It's not just miners who will have to adapt. Users will need to adapt to paying higher fees. This is a really important part of Bitcoin's design. We can't guarantee endless transaction growth, so we need to depend on scarcity of block space to force fees higher.

As long as demand is strong enough for perpetually full blocks, I'm confident the mining incentive can still work after inflation is done. This is an even more important reason to retain the block size limit than node or miner centralization.

[cryptjh]

One idea to pay the miners after 2140 would be a very small annual tax on so called dead Bitcoins. Bitcoins that haven’t moved for more than 130 years cut be forces to pay a very small annual fee. The Bitcoin would in all cases be considered lost, so taking less than 0.01% a year  from Bitcoins addresses that are considered lost, would help the Bitcoin system go on for thousands of years or more.

[abojamal]

What might the miners do at this junction?

Sure, they still get transaction fees. Would those escalate?

Might there be a reason to move to non-ASIC hardware?

Or a reason to change the reward algorithm?

I think the correct date is 2140 rather than 2040
With the low supply of BTC for mining the price will be very high
This is a market rule
supply and demand base.