In the original Rudolf from 1964 she was "The Doll with No Eyes." She literally had no eyes, but she'd still cry tears that came from the vicinity of her face where her eyes would be. Her line came after Charlie in the Box said, "Nobody wants a Charlie in the Box!" and she said, "...or a doll with no eyes!"

Nobody remembers this, apparently. I'm guessing it was deemed too horrific at some point, although it ran this way for a sufficient number of times for me to remember it.

When they put her eyes back on there wasn't anything left to be wrong with her, so they had to make something up. I don't recall what it is now - haven't seen it recently.