Can comedy cross a line?

Are "terrible jokes" actually terrible or are people just being oversensitive?
I think it is a bit of each--yes, such jokes are meant to be offensive and really cringe-worthy in general, but humor is an essential part of life. By taking everything seriously, we are never able to move on. You must be able to joke about your regrets and failures in order to recover from them.
If we did not joke about these things, didn't take them not so seriously, we would be drawn down by the heavy weight they put on us. There are people who are going to mean the sort of content that can be found in "terrible jokes". We must be prepared to take them humorously in case there is a time when they are not meant to be so.
Still, one must be sensitive with such jokes, as there are people and times for that sort of humor to be forgotten: it would not be appropriate to tease a victim of rape about their experience. But the terrible acts that humans perform upon each other will depress and terrify those who witness them unless they are somehow able to look at the situation with a lighter angle.
Not all types of humor are appreciated by all types of people, and it is important to be aware of this, but that does not mean that certain jokes should stop existing. Humor helps us move on with our lives and is essential in this way, no matter how awful a joke may be.