That one gives me nightmares.
Then my cousin died by suicide and, being my first encounter with suicide in the real world, it dawned on me that doing that in front of people was super, super not cool. I'll never know if I did that in front of someone that had lost a loved one to suicide via firearm.
You lost the statistical battle but most people will never encounter this scenario. We all encounter scenarios where we make a joke without knowing X person is going through that. You learn and adjust. For instance, I couldn't make jokes or references about cancer with a partner of mine because one of her friends died at like 17 to lung cancer. I was like, "Oh, alright. I get it. I'll avoid that with you."
You don't need to be disbarred from ever making the joke again just because you encountered someone who is sensitive to it. You just don't use that kind of joke with them.
But for me at least, it's worse when someone changes what they were going to say to try and avoid a topic they know might be sensitive to you, especially if it was in otherwise "innocent", organic conversation.
For instance, changing a joke with a cancer punchline to something else, on the fly, because halfway into it you realize it's going to offend one of the people present. Who certainly has already heard it, and knows what's coming.
Now, not only have you reminded the person of what you were trying to avoid, but you've also created this awkward tension where you-know that they-know, but have to pretend you don't know, because of the social "gesture" of changing their joke for you. Even if the fact that they're coddling you negates that gesture and then some.
The more extreme example of this is the scenario where kids in school are sharing stories about, eg, their mom or dad, and when you get to the orphan, you either skip over them, or ask them a completely different question than everyone else, without acknowledging and explaining why.
Suicide isn't so rare that we should avoid making affordances where we can. And even so, a true comic like Dave Chappelle can create real human even on dark subjects at the same time. It's a balance.
You are seriously digging deep into the "NO JOKES!" stance. Just because you did a joke that didn't go over well doesn't mean you can't make any jokes anymore.
And to be clear - because this is the internet and everyone on HN wants to be a pedantic andy - I'm not saying you go make "Dark humor is like a child with cancer. It never gets old." type of jokes to parents who had children die of leukemia or some shit.
But yes, making arbitrary rules about bad taste jokes is almost always useless.
Still, as a manager with responsibiliy you might want to restrict your toolbox of jokes by your conscience.