Yes, you are correct, sometimes when meditating when tired you can find more energy and sometimes you do fall asleep.
Meditating on the feeling of tiredness means to explore this thing called “tiredness” in detail. How does one know one is tired? What are the feelings in the body? What are the thoughts that go through the mind when one is tired?
Is there a constant feeling of tiredness, or does it ebb and flow? Where do the feelings come from? Do you feel the tiredness all over the body, or in particular parts of the body? Is it pleasant or unpleasant? What does this exploration of tiredness due to the thoughts of being tired? Is “being tired” one state, or is it many states?
There is really a lot to explore with the state we called “tired”. And it is very worthwhile to study in meditation.