It all depends on how bad the injury is.
Someone falling down a flight of stairs can get pretty F’Ed up. Slip and falls can be bad too. Insurance and the previously mentioned umbrella policy (it’s not too expensive) and common sense go a long way. Don’t serve alcohol to strangers.
If you allow BYO monitor strangers consumption. Some people get ALL JACKED UP at pinball events and don’t realize how much they’ve consumed.

I deal with some property management
And have seen some amazing claims over the years. One specifically comes to mind. A wedding ended at a place two blocks away from a bar/restaurant I do some work for. Some of the wedding aren’t done partying yet and head to the bar. One stumbly drunken woman misses the step up from the parking lot to the curb falls down and breaks her jaw.
Even with witnesses that saw her barely able to walk it was a two year battle.
She sued for $200,000 and noted that she wasn’t able to preform her duties as a wife as part of the lawsuit. Our lawyer said you can always tell the real scum bags cause they add that in.
Broken jaw =no oral sex for her husband.
Insurance paid for the legal bills and she ended getting $0 but it was a huge hassle.

I slipped on a icy walk a few years ago at a buddies house. It was a holiday gathering during an especially cold icy week and broke my elbow. The FIRST thing my insurance company asked was WHERE did it HAPPEN ?
I told them out at the end of my driveway getting the mail. I wasn’t about to let them harass my buddy and try to make his homeowners insurance pay.
Unfortunately SHIT HAPPENS!!!

I also went down a second time two days later out at the mailbox and didn’t go to the doctor for a week. So there’s no telling when I actually chipped the bone.
The entire state was covered in ice for two weeks.
Didn’t even need surgery just let it heal.
So it wasn’t more than a doctors visit and a follow up.
Are you of the same mindset of my neighbor whose son broke his hand playing baseball with the other neighborhood 10 yr olds in my others neighbors yard.
Sons father tried to latch his kids injury claim onto the other neighbors homeowners insurance to pay the medical bills “case his son was injured on his neighbors property”.
This is in a upper middle class neighborhood by the way.