Strange Smell in the Basement Walls – What Could It Be?

I recently bought a fixer-upper from 1979 in Appalachia with my husband, and we've run into a bit of a problem. There's this really strong, unpleasant smell coming from one corner of the basement, particularly around a weird cutout in the walls. The house inspector didn't find any mold or signs of rodents, and we've also checked for those without any luck. The smell hasn't been apparent elsewhere, but it seems to peak near those walls and sometimes even upstairs a bit. The previous owner didn't maintain the house well, and there were urine-stained carpets that we've cleaned up, but this smell feels different – like something might be rotting inside the walls. I'm considering getting an air purifier, but I'd love to hear if anyone has ideas or if I should be worried about this!