Wiktionary
n. (context idiomatic English) A person who is sick (mentally disturbed) in a morbid or gruesome way.
Wikipedia
Sick Puppy is a 2000 novel by Carl Hiaasen.
Usage examples of "sick puppy".
And she sits on my footstool, in my private chambers, in my home and dares to tell me that she will dose me like a sick puppy if I do not voluntarily take some vile potion that quack Pao has made up!
Don't you remember me telling you it was a 'sick puppy' that did this to Speedy?
Even as a young child, she was forever bringing home the sick puppy or orphaned kitten or, much to her mother's dismay, an injured wild critter.
I'm glad I haven't got the sort of conscience I've got to nurse like a sick puppy all the time.
Skip told Dearie and Dearie's new friends how we'd seen Stoke heading toward the Palace on the Plains from the third-floor lounge windows, how he'd fallen into the water, how we'd rescued him and taken him to the infirmary, how the doctor had said Stoke was one sick puppy.