Gary Lehrer heard that I like strange filling systems and told me about this pen, and this link was the only thing I know about it until another showed up in June 2022. It seems that the barrel likely had cotton or gauze in it to help draw in the ink.
Here is the text and picture from GoPens regarding this pen:
This 1924 La Plume D’Or is a very special pen. The Bibax capillary-fill Taper/Cone Cap in Red Mottled Hard Rubber is extremely rare. While the barrel is a hollow hard rubber tube, it is NOT an eyedropper-filler.
How on earth does this pen fill, then? There are four long slots in the back of the feed. The filling design is to put the pen, nib down, into an ink supply, and the barrel fills through the principle of liquid settling to its own level. The ink in the barrel now acts as the ink reserve.
Correct nib (medium) signed “D & D Paris 18 cts 3.” “D & D” stands for “Demely & Degan,” the founders of La Plume D’Or. Information found in “Une Affaire de Stylos” Quintette (1990) [in French language only]. Barrel imprint “Le Bibax B.S.G.D.G. Unis France.” “B.S.G.D.G.” is the abbreviation for “Breveté Sans Garantie du Gouvernement” which means “Patented without State Guarantee.” New-old-stock. Mint in original box (one end flap missing from box cover). Very rare, very collectible!