Rodents chew through wires
In order to assess the issue we had to open the wall. In doing so we found that rodents, who like to chew on old cables, had chewed through the cable attached to the outlet. This had also created a small fire inside the wall.
We recommended that we replace the wires, as well as the wall to remove the smell. We also recommended that they have the rodent issue addressed as soon as possible to avoid the same occurring in other parts of their home.