Solutions:
1. The Jackie Chan Approach: The hero can be kind of a major asshole at times, but they try their best and they're likable jerks. You want to see them succeed, but you wouldn't mind seeing some slapstick, even if it's fatal... This is very difficult to pull off, and a lot of American writers have preferred to put Jackie Chan into the roles of nice guys that you DON'T want to see getting hit. Jackie Chan understands this dynamic much better, and his protagonists are often dicks that get hit just as much as the bad guys, as they progress through the story and learn stronger kung fu, they become more mature and kind, making you really root for them when he stops getting hit and takes on the bad guy.
2. The Realistic Approach: Your protagonist is a regular person, and there's only so many times they can invoke the wrath of Cthulhu, get beat up by angry meth dealers, get forcibly injected with Giga Herpes, etc. before they just pack up and go home. Fuck this shit! I have other things to do in my life than adventure!
3. The Pacifistic Villains Approach: The bad men have enough shit on their plates already, what with that evil plan and all, without having to deal with the legal business that's involved with murder. When she's snooping around their shit, they have her arrested for tresspassing, or knock her out and send her home.
4. The Pokemon Approach: This universe has an alternate method of resolving conflicts that doesn't involve death. People get awful beat up, figuratively or literally, but once you lose this little game-duel, you've effectively lost at life and are considered out of commission until you're restored or something.
5. The Cohen Bros. Approach: Your character simply fails to complete the goal. It ends with everything sucking.
The world she's in should be safe enough to avoid it most of the time, since apparently you have to make several stupid decisions to get killed, so I'd assume it wouldn't happen enough for you to need the Jackie Chan approach, but it's always an interesting and fun thing to see, though, done proper.