There is an unused drain from a second story shower that I want to permanently seal. The PVC pipe that used to extend up to the drain is snapped off right at the threads from the trap about a foot below the floor. I can see through the hole it's a 1 1/2 inch pipe, but a proper cap won't fit since there's no pipe left to cap... Only the wider joint where the 1 1/2 inch pipe met the trap.

Since I have no desire to ever use this drain again, and even if I did I would have to fully replace the trap, I am hoping there is an easy way to seal this pipe without cutting out a portion of the floor and creating more work. If I drained all water from the trap and sprayed insulation / expanding foam into it, would that seal the trap long-term and be safe? There is a few feet before it connects to the main vent, so I'm not worried about the foam expanding too far. Is there some other way to seal this pipe without actually capping it?

I would attempt to remove the entire trap and cap the connecting pipe, but that also would require me to cut out a large portion of the floor due to how it's situated, and I would prefer not to go down that road unless absolutely necessary.

There are several proper ways to cap off pipe that is not in service:

1. Use glue cap
2. Use threaded cap
3. Use Jim Cap
4. Pour concrete into trap

Installation of caps requires some work space. As far as concrete goes - mix concrete and pour it into the trap .

However, if it is my house than I would do what ever possible to install PVC glue trap. Installed glue trap is the best way of sealing off old PVC pipe.

Let us know what you have decided to do. Back to you. Milo

Are you are saying that the trap is a glue up type trap and that the pipe out of the trap is broken flush with the trap, therefore you have no pipe to cap.

If that is the problem, get a 1 1/2 to 1" bushing, a short piece of 1" pipe and a 1" pipe cap. Cut the pipe to proper length so it will fit below the floor, glue on the cap to one end glue the bushing to the other. Then prime and glue the inside of the broken pipe left inside the trap and the outside of the bushing.
Insert the 1" pipe with the bushing inside the broken pipe in the trap.

PS
Tape your glue swab to a small stick to reach down into the hole to glue inside the trap pipe.

All good solutions. The best way would to cut out the trap and cap the drain line but the easiest would be to stuff rags down in the trap and fill the rest with cement.
Good luck, Tom