It is non-sensical. Let me put it in a tech analogy: Does a process exist only when it is scheduled to exist or does it cease to exist when it is suspended? No, right? Because the memory and execution context are still valid.

If the brain is a computer then the self is the software, the collection of code and data that comprise the OS and other available programs. This silly concept is saying "there is no operating system or programs, there is only execution and ram memory, when things are not being executed, they don't exist"

The data (our memories) and collective code (mind) that operates on that data, including code that isn't actively executing makes up a separate unique entity, separate from the execution state of the brain at a specific point in time.

Talk about missing the forest for the trees. Next science will believe the tree didn't really fall because no one saw it fall, even if you can see a fallen tree because falling and observing a fallen artifact are separate.