Once all the coins have been mined...

[JuniAiko]

Will BTC switch to PoS, or perhaps tangle like comfirmation?
Or something else?

I guess that would depend on the consensus of the community, but what is your personal take or preference?

[bitperson]

Given the state of the environment, the proliferation of nuclear weapons, the increase in multiresistant pathogens etc., I wouldn't bet on there being anyone around to mine that last coin. Even in a best case scenario from a human race viewpoint, 120 years is likely to change society very much and 120 years from now, Bitcoin may be regarded a museum exhibit from the old days when people still used currency.

[eminemcookie]

I would personally like to see the way bitcoin is mined changed at some point in the future but I doubt that will be the case. By the time the last coin is mined I imagine that mining will be very cheap because I suspect we'll have found some sort of renewable energy source. Given that assumption there's not really much need to change.