I'm not sure how it's supposed to work. Is everyone "stuck" in the Twilight Zone, yet strange things happen to only a small percentage of the population? Can people escape from the Twilight Zone?
The Twilight Zone is not a physical place, but Serling's term to describe the "dimension of imagination", where anything is possible, and your question assumes that only bad things can happen there.
By that yardstick, anyone dealing with a fantastic situation would be in the Twilight Zone. Whether that occurs in a place that couldn't possibly exist (asteroids with atmosphere, for instance), or whether that occurs someplace on Earth in a quaint little suburb normal in every other respect, that person could be said to be in the Zone.
The show in many episodes draws intentional parallels to the real world. If you're confused about what the episodes consider real and what the episode considers imagination, that's probably the point, and the creators would consider that a job well done. You're thinking about it, mission accomplished. It's not supposed to be a line drawn or a distinct border.
There are episodes where escape from the situation is definitely something to accomplish and go for ("Nick of Time", "A Penny for Your Thoughts"). There are others where, for the characters, imagination is the escape and that can be a good or bad thing ("The Sixteen Millimeter Shrine", "A World of Difference", "A Stop at Willoughby", "The Bewitching Pool", so many others). Others, escape is impossible ("Time Enough At Last", "Elegy") or the unreal situation is made worse by the nature of the characters in it ("Monsters are Due on Maple Street", "Escape Clause". again many many others).
While the plot twist that screws over the characters is a common bit on The Twilight Zone (although if you want a show that loves that bit, try the Outer Limits from the 1990s), that doesn't mean the Zone is a physical place that everyone needs to escape, nor that everything you see is completely in the realm of the unreal.
It varies per episode. In Little Girl Lost, with the girl who fell through her bedroom wall into another dimension, the hole closed up right after her father saved her. In Stopover in a Quiet Town, the one with the partying couple that wound up as toys for the giant boy, they clearly spent the rest of their lives in his toy town, unless they killed themselves.