My impression was that either this is something Monika made (which is doubtful, since she seems particularly bad at making new things), or this is what happens when you delete the sky files or ask the game to render a sky that doesn't exist. Her special scene is pointing to a null memory address, and the result is noise.

There's a lot about what Monika says and does that gets extra creepy when you think about in terms of memory addresses.

Like what she says happens when you close the game. She just starts to hear noise and voices before blacking out. That's because she isn't erased from your system memory when the game closes, she's just de-allocated. Your operating system will slowly reallocate her memory space with other files, overwriting her bit by bit.

Now, technically, she should exist in stasis during that time. She should just stop sensing anything the moment the processor stops devoting CPU cycles to her until she's reloaded into memory and can start using the CPU again.

That she still senses things indicates there is an essence to her that is beyond the digital. A sort of "soul" that resides in her memory address and can sense things even without a processor changing bits around. She's remembering things that were never recorded in her files, since the files were closed when they happened.

And speaking of files, since Monika is able to restore deleted characters, and still exists after being deleted herself, the implication seems to be that the .chr files are just links to the real character data (not the characters themselves). Instead of containing Monika, Monika's .chr file just tells the program where to find Monika. When you delete a .chr file, they still exist, they just can't be found by the program anymore.

So Sayori probably still exists somewhere in Act 2 and Act 3, the program just couldn't find her. But then we get into "what does it mean when a computer file hangs itself?" and I have no freaking clue.