Can a limiting reactant exist in a chemical equilibrium?

Limiting reactant

It's a matter of semantics. The limiting reactant is defined as the reactant which is completely used up leaving one or more reactants in excess. But in an equilibrium there are both reactants and products present. But it is possible to "tinker" with an equilibrium and deep shifting it to the right (by removing the product) so that eventually the limiting reactant will be used up.

For example, let us consider that overworked and oversimplified synthesis of ammonia.
N2(g) + 3H2(g) <==> 2NH3(aq)
Suppose that we ignore the fact that it's an equilibrium and select partial pressure for N2 and H2 which make H2 the limiting reactant. In the equilibrium there is N2, H2 and NH3, but if we cool the reaction vessel only NH3 will condense to a liquid and it can be removed. According to Le Chatelier's principle the equilibrium will shift to the right to make more NH3 and use up some N2 and H2. Eventually there will be no more H2 to react (since it is the limiting reactant) and the reaction will stop. (This is part of the Haber process.) So yes. In this case the limiting reactant is "existing" in a chemical equilibrium.

What are the choices?