Outside of the kitchen the wall is stained. There are no water lines there.
Only the drainpipe. There is no water. Do they have a machine that can detect? A leak under the floor. See picture

Hello Pastor1189,

What is on the other side of those two walls ? What is above this corner ? Is it exterior wall corner ? How far away is the closest plumbing fixture ? Is that "drain line" inside the wall ?

Back to you

Milo

It is next to the kitchen sink. No water underneath the sink. Drainpipe goes from the kitchen through dining room) to the bathroom, which does have discolored wall near the bottom moulding. This routing indicates the drainpipe. It happen years ago, had to dig up the floor in a certain spot. House was erected in 1957.

You have to be more specific. When you say "drainage pipe", what do you mean ? Large PVC pipe on the outside, buried under ground for rain water ? Is your house on concrete slab or raised foundation ?

Kitchen drainpipe goes into the dining room, to the bathroom to the main drain and out to the septic tank. 10 years ago the pipe did break in the dining room and they fixed it with a rubber shielded coupling. The pipe is make of metal. Probably rusted out in spots. Concrete slab

I am sorry, I don't know your house. I assume that "drain pipe" is under ground, not traveling from 2nd floor down that particular wall. Correct ?

If so, there is probably small chance that wetness is coming from underground pipe, that is probably buried at least two feet under the house. There is no pressure in drain pipes and water flows on the bottom of the pipe, rarely filling up entire diameter of the pipe

It doesn't appear the baseboard is really wet. When you touch it - do you feel it is wet?

Check on the outside of that wall. Is there sprinkler close by ? How about garden hose valve ?

If it is next to the kitchen sink - than there must be kitchen sink drain in that wall. That drain may have a leak. Moreover, if there is a drain, there must be a vent that vents kitchen sink drain. Water may be traveling down the vent pipe from the roof, from deteriorated seal around the pipe and flashing .

Also, do you have wall mounted kitchen faucet ?

Back to you

Milo

You got it. The kitchen drainpipe goes directly over that spot. That doesn't appear wet.
But it may be small leak. Could use a moisture meter. Another discolored spot appears in the bathroom near the door, similar to the kitchen area. Insurance company wouldn't appreciate digging up the ceramic tiles, to fix it. Just a regular faucet. I may remove a portion of the molding to see further