Asking quite a bit from an elastic substance. Whatever you want it to do, it also has to taste good and be non-toxic. Gum as it is would probably degrade better if people didn't just toss it on the sidewalk. There's also quite a bit going on with teeth—despite their appearance, they're actually quite porous, especially if you haven't been brushing.

Most sugarless varieties of gum supposedly improve tooth health, but I'm still wary of the artificial sweeteners.

Quick drying/hardening chewing gum - Gum which dries or elasticity when exposed to air. The best alternative is to supply a disposalpouch along with the gum. It should be made mandatory to sell chewinggum with disposal pouches.