I think this is a very useful example of something I don't have a name for, other than a "how should I use my hammer on this screw?" question.

It's a perfectly valid question, but it contains what I think is an erroneous assumption -- that it's special characters inside $path which are causing the problem (and also that "%" is a regex special character, but that's a minor issue). So people are trying to help you with the \Q and \E, but that may just be confusing the issue.

Special characters in $path can't "damage" your regex at all, Hotshot, they can only enhance it. They might enhance it in ways that give unexpected results, but they shouldn't be causing that error message.

Your problem is that you get the "Use of uninitialized value in regexp compilation", period.

Like everyone else, I think you should check what's in $path before you do the regex, but I just wanted to get a bit meta on this question, plus call attention to your misapprehension about the percent sign.
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“Every bit of code is either naturally related to the problem at hand, or else it's an accidental side effect of the fact that you happened to solve the problem using a digital computer.”
M-J D