in practice, if the prime minister were to spontaneously combust, or
disappear into the woods with a group of yeti and never be seen again,
and he'd probably think he was meeting chewbacca, the dunce, but if
he were to disappear or evaporate, the party would choose an interim
leader and launch a leadership process, and the convention would be
that that interim leader would not run for leader in the pending
process (as that would give them undue influence).

but, in case of emergency?

it's actually the supreme court justice that takes over.

https://en.wikipedia.org/wiki/Canadian_order_of_precedence