My first point stands, I am afraid. And that example is not a matter of style vs grammar. Style debates are things like split infinitives, Oxford/Harvard commas, and how best to use certain types of punctuation, spacing, or even double negatives. And yes, these change based on time and context.
However, grammar rules exist for a reason—for consistency of understanding. As someone rightly raised, they are not laws, as they can be disregarded if your intention is something like a piece of poetry with open-ended meanings.
On proverbs and sayings not conforming to normal English rules: this is wrong. Even direct quotations should be amended (with notes or techniques like additions in square brackets or ellipsis).
In any case, “rat trapped in a cage” is neither a proverb nor a famous saying, but a bog-standard figure of speech. “Caught like a rat in a trap” is probably what you are thinking of. I will use that to illustrate my original point.
Which feels better?
1. Bill, Bob, and Ben had nowhere to run. They were caught like a rat in a trap.
2. Bill, Bob, and Ben had nowhere to run. They were caught like rats in a trap.
The first should produce a sort of mental jarring as you have to equate the subject of 3 men with the subject of 1 rat. It is possible to equate 3 men with the plight of a single rat. But the second case is not only grammatically correct but also easier to mentally digest. If in doubt, following the standard grammar rules will give you more chance of avoiding misunderstanding. I tried to make that last sentence sound less patronising but failed, sorry.
(Remember also that a lot of English is read by non-native speakers, who do learn grammar and so expect things to match or it might throw them. It will also throw off translation software too.)
Incidentally, I teach this stuff and edit for a living, so apologies if this sounds like a bloody lecture.