As long as one person keeps running the old software, the old chain is alive.
Even if nobody does it, somebody could start running it again at any time.
The different chains will have different market caps. And the general public will forget about chains that have sufficiently small market caps.
I wonder what will happen to Ether that is in custody. Like in the Greyscale Ethereum Trust or the 21Shares Ethereum ETP.
Has anybody ever checked the TOS of these companies on what will happen if multiple forks carry significant value?