Analysis of free goods
You can imagine a demand curve continuing through the x-axis as monetary price becomes negative. A negative price can be interpreted as payment to pick up shirts, a kind of subsidy.* That might tempt those who are still unwilling at price of zero because there's still a opportunity cost of picking up the shirt, or because they only wear collared shirts, or because disposal is not free (the unwanted shirt would need to recycled).

In the simple model, the demand curve that represents willingness to pay is holding these other factors fixed. In a more complicated model, the price drop might induce congestion at the student union, so the demand curve would also shift down or up, depending on your desire to spend time in a crowd of college students.



*Obviously, you have to impose some sort of limit per student to keep quantity demanded from shooting off to infinity.