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.
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.