This is very possible. Shorten the room by just the width of a stairway, and build one going down behind a false (non load-bearing wall). A full stairway makes it much easier to access for storage, and is useful if you ever decide to finish the area as an added part of the house.
And you can have built-in bookshelves or cabinets into the part of the wall above where the stairway is lower down, so you don’t lose that space. And the part of the wall near the top of the stairway is a good spot to mount a large-screen TV – the wires & cabling can be easily put behind the bare wall, out of sight.
What you need is a bust of Shakespeare on a table. You tilt the bust back, hit the button and the wall slides open, revealing two poles marked “Bruce” and “Dick”.
The problem is finding a customized Lincoln Futura to put in the basement.
I lived in a house with a trap door, once. We always assumed that the place was built by drug dealers because it was nice but also had its quirks! The trap door opened to a ladder which led down to a door on the driveway. In the event of a home invasion this would be a sneaky way to avoid capture. We never actually had a reason to use the trap door or the ladder.