Similar to the plant Jinx in Larry Niven's "Known Space" books, a planet with a "fossil tidal bulge" could have "ends" -- inner and outer (or East and West, as in the books) poles -- that stick up out of the atmosphere -- this could produce a high density/pressure atmosphere near the horizon zone (twilight zone for an "eyeball" planet of a red dwarf, or where the primary is on the horizon for a moon of a hypermassive gas giant as with Jinx) -- while the "ends" have an Earthlike atmosphere, or even no atmosphere surrounded by a "ring" of habitable pressure and composition.
Formation of such a bulge would require the planet's/moon's orbit to have moved away from its primary over time, after the mantle and core have cooled enough to limit the amount of adjustment for the reduced tidal stretching. My limited understanding is that this is unlikely, give what we now know about tidal heating (the engine that keeps Europa's ocean liquid, among other examples), but I'd hesitate to call it impossible -- and the unlikeliest things happen if you look long enough.
Comments noted that the atmosphere will remain mixed, so the twilight band can't be a toxic composition -- but it doesn't need to be. Plain air will kill you fairly quickly (from oxygen toxicity) at not much over 7 atmospheres (and nitrogen narcosis might make you make a fatally bad decision at 2/3 that figure). Sure, there could be local critters that adapt to that -- but the very air would be deadly to wandering humans from the 1 atm. zone.