On Error persistence?

[Gates Is Antichrist]

Can someone explain the persistence of On Error, both:
forward (calls from the sub/function), and
backward (after returning from[i.e., exiting] the sub/function)?

So I'm asking, what can happen if you don't add On Error GoTo 0? Doth pain awaiteth from not cleaning up after thyself?

 

[Legacy 98055]

Bubbles up the stack from the called to the caller.