Arsenic and Old Lace includes discussion of torturing someone to death with the "Melbourne Method." Details are not provided, but it is implied to be quite gruesome.
In the live-stage version of Disney's Mulan Mushu has been demoted from his pedestal because of an incident involving "Confucius, a silk worm, and the near downfall of a dynasty!"
The movie has a bit of a Noodles Incident for that as well, with them alluding to the last ancestor Mushu assisted and then showing a spirit with a decapitated head. "Yeah, thanks".
In the Tony-nominated play Next Fall, a main character's mother is talking about his childhood, when she suddenly interrupts with the following lines: "Then I went to jail for six months...for selling pot... [sees incredulous look on listener's face]...it's a long story involving my ex-best friend. A one-armed hairdresser from Scarsdale, I kid you not."
In Into the Woods, the Baker's parents supposedly died in "a baking accident."
In Chicago, Velma's number "I Can't Do It Alone" is an in-universe Aversion. She's trying to convince Roxie that the Kelly Sisters' Double Act is too fantastic a chance to pass up on, so she demonstrates it for Roxie — but it just doesn't really make sense. It gets especially funny on the Revival cast soundtrack, where the listener only gets hints such as "See? I kick really high!" and an enthusiastic "SIDEWAYS!".