My elderly friend swears she has a sticky substance in her mouth all the time. Has anyone ever heard of this?

Poor lady! I have a terrible problem with dry mouth caused by medication. Occasionally, my teeth feel what I call "fuzzy". The dentists think I am nuts, also! But first, I take care of the dry mouth by chewing sugar-free gum. The dentists encourage this. I also use a mouthwash made for dry mouth, and change my toothbrush frequently.
What helps the most when my teeth feel hairy (lol, sometimes it does feel like a hair is in my teeth!) is a good anti-bacterial mouthwash, sometimes watered down a bit, or good old salt water rinse. A good teeth cleaning by your hygienist is always in order.

The main thing is, she isn't "nuts", I don't know why dentists don't recognize this problem, but tell your friend she's not alone! Good luck!

What kind of foods does she eat?   How much fluid does she drink?  Is she on any kind of special diet?   How often does she brush her teeth or gargle?

Is it possible that this is sticky saliva that comes with dry mouth? Dry mouth is very often related to medications. There are mouthwashes, sprays and even little adhesive discs that help with this.