If you're using the Noxzema every day, probably like your mother did, and you're getting small drops of water in the jar but covering it, then it softens noticeably. (This without glycerin.)
When I open a new jar I usually return the lid daily. But as I get water in it - I'm doing this in the morning shower - I start using the lid and storage position as a control mechanism for the cream. When it's too soft for me I store the jar upside down on my wire rack with the lid off until the next morning. After a while it becomes subconscious.
The only caveat is that if you let a jar dry out and get crunchy I find it impossible to rehydrate properly. It's a goner.
This makes sense. If it was too "runny" in the first place and then water slowly got added to the container from using it, it might reach a consistency in the jar that folks wouldn't like.
It does dissipate/melt/soften/whatever really quickly upon contact with water. I thought perhaps it would gunk up my razor but it never has. In fact, it seems to leave less residue on the blade than any of the other creams/sticks I've been using. Due to our water here, I have to take my razor apart after every shave and throughly rinse and dry both the razor and especially the blade. Usually when I remove the blade right after shaving, it has a slight white film on it. When I take it apart after using the Noxzema, it's still shiny.