For us, the biggest stress here would be the stress of being kicked and punched repeatedly in the solar plexus. We aren't fighters.
Most fighters become fighters because they love to fight—they thrive on the contact, the competition, the abuse they inflict, and even (for certain fighters you probably don't want to mess with) the intense physical pain. Since it takes a pretty fearless person to jump into the ring, most career-related stress isn't directly associated with the fear of injury.
Much of the stress comes with the financial situation. After all, this isn't the greatest-paying job in the world. Many unsigned fighters are lucky to make a few hundred bucks per fight, and even undercard UFC fighters have to figure out how to stretch a measly couple thousand dollars over the course of a year.
Then there are issues of anxiety when, for example, an injury sidelines a fighter for an extended period of time. No fighting, no money making—not to mention the rising hospital bills. This is why you want to put a little bit of that money in the bank and not spend it all on tank-tops and tanning lotion.