EDIT It was pointed out in the Answers-section that I am confusing k-means and kNN. Indeed I was thinking about kNN but wrote k-means since I'm still new to this topic and confuse the terms quite often. So here is the changed question.
I was looking at kNN today and something struck me as odd or - to be more precise - something that I was unable to find information about namely the following situation.
Imagine that we pick kNN for some dataset. I want to remain as general as possible, thus $k$ will not be specified here. Further we select, at some point, an observation where the number of neighbors that fulfill the requirement to be in the neighbourhood are actually more than the specified $k$.
What criterion/criteria should be applied here if we are restricted to use the specific K and thus cannot alter the structure of the neighborhood (number of neighbors). Which observations will be left out and why? Also is this a problem that occurs often, or is it something of an anomaly?