Does urine make concrete hygroscopic?
Very interesting question - and thorough. But I would like to get proof that the spot is due to moisture. #1 Does the spot grow and shrink dependent on the relative humidity at that position? #2 If the spot is misted with a water sprayer, is it sharply defined? #3 If the spot is gently warmed with a space heater, does it disappear? #4 What color is the concrete? Very light (low iron), medium gray (medium iron), or dark, or brown?
If multiple cat pees have been located there, it's possible that attempts at cleaning or deodorizing have also been applied to the carpet, and have soaked thru and into the concrete. At this point, so much could have happened to the cement compounds that you and your parents should consider yourself fortunate that the deviation from perfection is only visual and not oderiferous! I have a spot on an outside patio that is dribbled upon from an aluminum gutter, only occasionally, when it rains (the end cap on the gutter has a tiny leak). The spot is about 4 inches in diameter, and is only visible at certain times (usually high humidity, like when rain has almost completely evaporated). Without a microscopic examination, I can't see anything unusual, but I suspect that some of the $Ca(OH)_2$ in the concrete has been dissolved, or perhaps carbonated more, or both, and the water in the pores at that spot is slower to evaporate.
If the discoloration is obnoxious, you might try painting (or dusting) that area with a non-paint paste of calcium carbonate in water. It would be harmless to the concrete, but provide some lightening. But then the area might be too white...