A kind of cup that does not hold water is a "cupcake." This is a wordplay riddle where "cupcake" refers to a small cake baked in a cup-shaped paper or container, which obviously does not hold water like a drinking cup would.
Another interesting type of cup that demonstrates a unique behavior with liquids is the "Pythagorean cup." This cup looks like a normal drinking cup but has a siphon mechanism that causes it to drain all its liquid if filled beyond a certain level, effectively not holding water if overfilled intentionally.
So for a straightforward riddle answer: a cupcake is the classic answer. For a more fascinating example with scientific and historical context, the Pythagorean cup fits as a "cup that does not hold water" beyond a point.