As Copyright said, "in the stairwell" - though that doesn't tell us whether he's at the top or the bottom, or on a landing (or on the stairs themselves) somewhere in between. His actual location would need to be specified.The burglar was waiting at the stairs/staircase/stairway.
Meaning: he was in the area where
isthe starcase to all floors is.
What's the name of the space where
isa staircase in a big building is?
To quote Heinlein:Really? What do you do when the power goes out or there's a fire?