Dana Angluin's L* algorithm - Hypothesis inconsistent

Question

is it possible for the Dana Angluin's L* algorithm that a hypothesis is inconsistent?

So assume we have a closded observation table for a regular language L. Now after creating the hypothesis we will get a counterexample w.

The Question is: Can the counterexample w be chosen in the hypothesis, so that I have two times the same counterexample?

Unfortunetaly I could not find any language and counterexample where it will work.