The most common and most likely answer to this crossword clue is the 7 letter word RAGDOLL
I've seen this crossword clue in Independent
R
A
G
D
O
L
L
More clues leading to the result RAGDOLL
Buddy explains!

The straight part
We know that "toy cat/ (7)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case toy cat/ (7) = ragdoll.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does RAGDOLL mean?
RAGDOLL noun- A modern American breed of domestic cat that relaxes completely when picked up.
- A model consisting of a set of connected rigid bodies that can collapse in a loose, natural manner.
- To be flung about, such that a person has an appearance like that of a rag doll that is flung about.