Would btc be liquid ? How would you even send and receive even if you do own the private keys to your coin?
I am aware that the internet is man-made, Bitcoin is also man-made, honestly I will not compare Bitcoin to gold, Bitcoin and the internet can be lost, but gold is not, Bitcoin appeared in 2009, gold appeared centuries long before Bitcoin appeared, that's a sane thought.
If you say the internet is dead, of course all the access that humans currently use is destroyed, there is no exception: those related to the internet disappeared, not only Bitcoin, almost all sectors were destroyed, for that before that happens use the internet and Bitcoin as well as possible while you can still use it.
Actually i can't vouch for myself on this question, whether i live or die, before and after the internet dies.