Either a forced perspective illusion, or the same method used in a bottomless pit. The first being the most simple. A painted covering at the point you want to block the hallway. This will make it so you have some real hall space to start with. On the canvas, you paint the hall to look like it is receding by making it progressively come to a small focal point. The later, this would require framing in 2 panes of glass, lexan, plexiglass, and coating the inside glass with mirrored window tint. Havering a door within the framed sheets with some mellow lighting, will make it so the door ( or whatever is in between the 2 panes) will keep reflecting off each piece, giving the appearance that it goes on forever.
to bad it wasn't wider it would be great for a mirror maze but icepick has the right idea the only other way i see pulling this off is projecting a picture of the hallway on to the far wall but the mirror behind a two mirror or glass with privacy film like icepick said is the best way to go