I believe this is generally attributed to clashed dies that give the impression of a single fold of drapery. In Volume V of Bill Bugert's books on seated halves he mentions this about 1839 no drapery halves for WB-1 on page 24 as follows:

LDS “With-Drapery.” A few LDS examples of this die marriage have what appears to be drapery
below the elbow on the obverse die. This “drapery” is actually clash lines and can be very
deceptive. In 11/2015, I noticed an AU53 TPG 1839 of this die marriage that was mislabeled as a
With-Drapery type. The clash lines below the elbow obviously led the graders astray.

I actually own the AU53 no drapery example that Bill references and was able to cherry pick it for the price of a with drapery coin.

The "partial drapery" thing is nothing more than clashed dies on the die. It's a die state, not a variety. There might well be something like that here. The eagle's wing could be involved.

A Not Drapery Half Dollar.