nail through romex copper wire
Known damaged wires in a hidden location? Not a good idea. It could be "just on the edge" such that movement over time will eventually cause arcing and a fire.

The best thing to do is to replace the cable. The problem is that you can't simply wire-nut in a section of cable. The connections need to (a) be in proper junction boxes and (b) accessible for maintenance. Inside a floor or under a baseboard is not considered accessible. Your options are:


Replace the entire cable from the receptacle back to the next junction box (which could be another receptacle or the main panel or sometimes something else). The problem is that it can sometimes be quite hard to do this.
Splice using connectors certified for hidden use. See [Is there a way to simply splice in an additional length of 12/2 NM-B cable? for an answer that is one possible solution.
Replace the cable with a cable going a different, easier, route, such as connecting in to another nearby circuit. The catch is that if your refrigerator is on a circuit by itself, you may want to keep it that way to avoid a number of possible problems.