If there was a period of time with no transactions, what would miners have to do? This question is similar to a few others, but I haven't gotten seen a clear answer anywhere.  It came up as I was trying to explain mining to a newcomer.  And he asked: "If aliens came and put all humans to sleep ( and any automated transactions that may have been setup ) would miners have anything to do?"  

So the question is, if zero transactions are happening, are miners still mining? And if yes, what exactly are they doing?

I explained also that eventually block rewards will end, so I'm looking for an answer that is agnostic of the bitcoin network now vs the post-block rewards bitcoin network ( after the 21 million are "mined" )
They would mine empty blocks. Block difficulty would remain the same.

Would they have an incentive to mine blocks? In the year 2140, all mining rewards will be from fees. If there are no transactions, there are no fees. Between now and then, rewards will step down over time. So either:


Clients will keep mining.
Clients will stop mining because there are no transactions.


I recognize that this is a useless answer (maybe they will, maybe they won't) but I hope you understand the difficulty of predicting what mining clients will be like in 5-10 years.