Where do the come thru the wall on the interior side? Pictures from inside?

I don't believe the pipes actually come through the wall rather I believe they are included as part of the poured foundation. I'm not sure that the musty smell and those pipes are related. The musty smell is coming from the carpet in a corner of the house where one of the pipes is located however I can't fine any source or evidence of moisture.

How could they be part of the foundation? The foundation is only 8" to maybe 12" thick and there is no reason for pipes just in concrete, they to come thru.

So, you think it would help to identify the pipe if we knew where they went on the other side of the concrete wall?

Novel concept!

I have no way of seeing the pipe from the inside of my house. The house is built on a concrete slab so the pipe doesn't come through any wall. It appears that the pipe was ran first and then the concrete slab/foundation was poured over it. The pipe runs underneath my flooring which I'm not going to pull up just to find out what the pipe is.

Oh it is a slab you mentioned foundation implying a basement. No clue than or ideas.

You can also rent a 'sewer cam' to look inside it. You could probably drill or punch out a hole in that foam to look from the other end.

The wet spot may be completely unrelated. Any plumbing anywhere near the wet floor? Check all your faucet plumbing etc.