I've heard this referred to as "catroofing", though it's probably a very localized expression or I'm not remembering it correctly since I can't find any references online.
In any case there's a good origin story:
There’s an old joke about a guy who went away for a long trip and asked his brother to take care of his 16 year-old cat during his absence.
A week or so into the trip, the guy calls home to check in. He knows his cat is elderly and he’s concerned about it.
“How’s my cat?” he asks his brother.
“Your cat’s dead,” his brother tells him.
The guy is upset. “This is how you break it to me?” he asks. “This is how you give someone bad news? How insensitive can you be?”
His brother is, of course, sorry, but can’t help asking: “What was I supposed to say? The truth is the truth.”
“That may be,” the former cat-owning brother says, “but there’s a way to give someone bad news more thoughtfully. You should have psychologically prepared me for it.
“When I called, you could have said, ‘your cat was crawling on the roof of the house when he fell, and I took him to the veterinarian. And then, next week when I called, you could have said, ‘your cat’s not doing so well’. And then the third week, you could have gently broken the news. That’s all it would have taken. Just a little bit of kindness.”
“I’m really sorry,” the brother say. “I’ll do better next time.”
“It’s OK,” says the other brother. “I’m just upset. I really loved that cat. Anyway, let’s change the subject. How’s our grandmother?”
“Well,” the brother says, “she was crawling on the roof of the house …”
Ref: https://www.thenationalnews.com/opinion/first-tell-me-about-...