You can make a living off of jazz in the same manner a classical musician makes a living off of classical music. Understand that this may include playing in a functions band, teaching, composing, working in sales, grabbing any session work you can find, and having to constantly hustle in order to keep it all going. If you're lucky, you land a regular gig with a large corporation (cruise lines, disney, 6flags, etc). Heck, I know a jazz drummer that plays in a Doors tribute band to make ends meet.
If you also get a BM degree, you can run the functions band, studio, shop, etc.
Alternatively, you can do as I did and build a career in some other discipline. You're then free pursue music as a hobby.