Sweetie and I loved this humorous display on the history of invisiprims.
Above, leftomost, you can see the prototype-- a regular plywood primitive. Then it's gone (hence, invisiprim) until 2009 (in the distance), when you can catch a glimpse of it due to a supposed glitch.
As you no doubt know unless you're relatively new to Second Life, until the introduction of alpha masks with Viewer 2.0, invisiprims were used to hide parts of an avatar's body. They were widely used in furry communities and by makers of high heels.
Invisiprims worked fairly well, but they had a difficulty-- objects with alpha, including the waters of the seas of Second Life, are rendered invisible if they are behind an invisiprim. That's why there appears to be a hole in the water when you hover over the oceans in your legacy 7" CFM pumps.
I didn't know this until I read the wiki above, but there are two special invisiprim textures, "38b86f85-2575-52a9-a531-23108d8da837" and "e97cf410-8e61-7005-ec06-629eba4cd1fb", which can be set only via script. No wonder I was unsuccessful at my shoemaking endeavors!
Invisiprims were rendered obsolete with the advent of alpha masks, but still worked. Deferred rendering (enhanced light sand shadows) breaks them.
A lot of legacy furry avatars and shoes use alpha. In the case of the furries, I should think, simply wearing a full-body alpha mask would fix the problem-- except I'm sure the invisiprims are attached to the various body parts and would require some degree of skill-- and modifiable body parts-- to trick up. Ditto for shoes.
I now include an alpha mask with my robot avatars. I didn't use invisprims before (mainly because I didn't know how to make them. Instead I used a body crusher animation to keep arms and legs inside.
I suspect a lot of my shoes will be broken when the new materials rendering system comes online (and I believe it just did). That's sad.