Actually no. If btc price falls to 1$, no one will mine btc because it would cost them lots of money to do so. If nobody mines btc, no transaction can be done. If no transactions can be done, it's hard to call btc "alive", cause it doesn't do anything.
If bitcoin goes below a dollar, people will still mine and run nodes.
I gave an undervolted S1 to a friend after my upgrade.
I didn't sell it, probably won't and I'd venture to guess that many enthusiasts
have their own way of supporting the network, should such a time come.
Right now, that you can make money with bitcoin is an interesting feature
(ok, ok I love that feature ;-)
BUT
I'm willing to follow "this experiment" to the point when it IS money or nothing.