I know exactly what you are talking about... It took me a minute or two to get out of there... If you just keep crouch jumping and sprinting eventually you will escape but it is just trial and error... I screwed around with it for like 2 minutes or so and I was finally able to get out of there... Also if you have any weapons that can kill you, use them because if you die you will respawn somewhere else.
If all else fails you can generally just reload last checkpoint and you should spawn somewhere else although you may have to go back and flip the switch again... That happened to me on my second playthrough so apparently it wasn't glitched the first time through, so maybe if you just reload the checkpoint it might unglitch the stairs.