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."
Also from Into the Woods, the Witch's exposition rap in "Prologue" reveals that after the Baker stole her magic beans, something happened that caused lightning to flash and presumably more weird stuff. She doesn't elaborate on it any further and dismisses it as "another story".
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!".