Oh poor Olivia, that's so sad she has that problem. I really hope she gets better soon for you.
Maybe your vet can shave that wet fur off, that's going to end up causing her more problems like red sore skin. Too bad she can't wear a drool bib, is that possible I wonder.
If that green discoloered hair is not from her pellets mixed with her saliva, than it must be like mold growing, but it's not the same as the fungus (ringworm)my pigs have so don't worry about that.
The only reason I know this is because I was a dog groomer and have seen many slobbery dogs with green fur from being wet all the time.