How literal is this? To use an example, we'll use the show Ridiculousness. If someone gets hurt, but is okay, which seems to be the case in every episode of the show, then that would still be funny, but if they end up having to go to the hospital or worse... dying, then it wouldn't be funny?
Something can be funny to someone regardless of them being "alright or not", even in drastic cases. It all just depends on what that person in particular finds to be "funny". There is no set in stone formula for what is funny, and when things should or should not be funny.
This could apply to a lot of things whether it be physical, emotional, or literal. Not to mention each person's view on what they find "funny" and "hurtful" is also on the line here as well. In my opinion, the most common use here is the literal sense. Everyone likes to crack a joke or two. However, the more offensive the joke is, the better it is for getting a better reaction out of people whether it may be good or bad. Most of the time, people aren't too offended by the jokes a person makes, but a simple misplaced word can send a person into a fit of uncomfortable nerves or even a fit of rage.
While comedy is subjective, there are certain subjects that should not be used lightly. It's best to get to know what a person's comfort level is before you start. I mean, common sense comes into play a lot here. You're not going to crack rape jokes in front of a rape survivor( or at least I hope you wouldn't!) because you don't know how they're going to react. [And rape shouldn't really be a comedic topic to begin with but that's another discussion.] Because there is such a thing as tact and respecting other people's boundaries. Words can have just as much effect on a person as physical blows, perhaps more of an impact. Broken bones mend and bruises fade. But the effects of words can last for years.
I suppose I should clarify for everyone: I was talking more about physical pain. Using Ridiculousness again, there are a variety of things: people's skateboarding fails and having their skateboards hit them in the nuts or butt crack, general falling down, etc. It's only temporary pain and they are able to walk away. There was one episode where they showed a uni-cycling fails clip package. I'll let this video explain it (just watch until 1:30):
