This sounds like the kind of applicant who would complain that fizzbuzz has no real world application. Despite the attitude in that article, there are real applications of cycle detection.
It sounds like the kind of applicant who understands the problem far better than the interviewer. So go on then: once you have detected it, what algorithm would you use to repair it? Wouldn’t you consider its existence to be a bug in the way the list was constructed?
It depends too much on the context to give a general answer what to do with it. It can easily not even be an "error," like in the first example on this link where you're simply testing the strength of a PRNG. Another would be if you're writing something to represent reals in decimal and you want to see where your number loops, like 1/7 = 0.(142857).
Examples where it's not desired, and what to do: Detecting infinite redirects in browsers and stopping the loop. Detecting thread deadlock and terminating the process. Detecting looping references in an Excel spreadsheet and showing #ERROR in the cells instead of letting the process hang forever.
https://en.wikipedia.org/wiki/Cycle_detection#Applications