I'd get an experienced plumber in there before anything else.

Does the drain work? Does there seem to be leaking from the pan into the slab?

We ended up replacing everything in my 1965 house except right where it comes in and goes out of the house once we had everything open. Luckily it was all concentrated in one area.

Our cast iron stack developed a hole or small split.

Looks like great place to not put a bathroom.

What else is on the lower level with this old bathroom? Bedrooms? Is it a walk out basement?

Was the drain blocked off when the closet was built?

Is their any possibility it was taken out due to flooding or backups?

Many houses in my neighborhood have kitchens in the basement and some have bathrooms. They also have rain water diverted from parts of the roofs into stacks that go through the house. The houses with showers in that basement area will sometimes flood through the shower drain during a torrential rain. This is because the neighborhood infrastructure is so old that storm water and sewage go into the same system and rain water, if it backs up into the internal stack reaches a "level" that is higher than the level of the drain in the shower. This is not sewage back up, I've seen it, it's water with shingle particles and leaves in it.

Anyway, some of the houses have had their showers in the basement removed.

On the other hand, where I grew up a basement shower with the pan and drain cast into the floor was not uncommon. Men would come home from the factory, go straight to the basement, and take a shower.

There's no way I can tell from a single photo whether this is a bad place for a shower or not, I am not as omniscient as Skil who also seems to despise anything original to a house as far as I can tell.