I guess this is a more likely (but still far-fetched) scenario when trying to apply to PhD programs and needing funding? If you're an old fart like me just trying to get your MS and some research experience after a decade or more in "the real world." I'm having a hard time seeing any institution saying, "Nope, we don't want your free money and labor." Unless your SOP and LORs were written in crayon and your GPA puts you in the squares club!
Although, I suppose if the 2 Universities that I have applied to don't want me, I'll just go down to the pub and have a beer and start working on next year's applications. Who knows, maybe by the time my own kids are at Uni I can be their TA hahahaha!
If it does make anyone feel better, I will relate a story of one of my High School teachers. She let 30 years pass between her MA and PhD and she taught HS for over 40 years. She's since passed on, but I remember her remarking that we shouldn't be in such a rush. It's the journey that matters. So if you end up spending time in the real world with the rest of us, please don't despair.