Matching user-input text with a user-input regex in Node.js

I’m assuming that DoS is a possible issue when matching, on the backend in Node.js, arbitrary strings with arbitrary regexes with one of JS’s regex functions. If the provided regex is simply invalid, the error thrown by the constructor can just be caught — but I’m thinking it’s possible that matching the string with the RegExp could become a significantly or even completely blocking operation, deliberately or accidentally by the creator of the regex and the string? If so, how exactly would this be caused, and how could it be mitigated?