How does the limiting reactant change?
A reagent either is or isn't "limiting".
A reagent capable of a reaction will react. The "limiting" aspect has only to do with which reagent has more available material. The one with the least material (stoichiometrically) "limits" the reaction by being used up first.
So for example, if you react hydrogen and oxygen to form water the stoichiometric balanced equation is:
That means it requires two moles of hydrogen for each mole of oxygen for a complete, 100% reaction with no limit on the production of two moles of water.
However, if you ONLY have ONE mole of hydrogen, only half of the oxygen can react, and only ONE mole of water can be formed. That will leave some oxygen floating around after the hydrogen is all gone.
Thus, in this case, hydrogen is the "limiting reagent".