Its generally only a thing in stories of Hugbox rescues or Abuse/Sadbox Hellgremlins.
Traditionally writers make some more empathetic or make it a Feral/Domestic divide, but general Fluffy lore is any sign something is wrong from mental to physical disability or even undesirable aesthetic traits are a “Dummy” and are subject to as severe of abuse as if they were brown, though are less likely to be forced to eat shit.
Mothers and siblings are likely to kill them, they are excluded from all activities, berated constantly, subject to any violence or sexual assault, and will go unmourned and immediately forgotten.
Why Toughies can suffer such damage and be accepted, why Sensitive and Derped are different from just neurodivergent, why Pillows or Litterpals are seen as different, and other contradictions is up to the creator as well.
Generally a Bestest is exempt from being a Dummy and in fact the mother may treat the “normal” (can’t recall the modern term) worse as a result of increasing damage to the Bestest, though the Dummification of a Bestest via broken or missing limb, stutter, missing ear, going bald, and so on may result in a mother cycling through the undamaged Fluffies as the Bestest until settling on the least damaged in spite of other factors or just abandoning them all to start over. Maybe cheerfully, like she genuinely no longer loves them and thinks she’s free from them. I dunno.
I like toy/capitalism metaphors, so they’re like toys missing accessories, with broken gimmicks, lost limbs, general defective traits, fucked up paint, or a Barbie with fucked up hair. Maybe its more endearing, maybe trash. Should be based on the story and individuals.
Hell, decent scars or a limb with a clean loss may be more endearing to Fluff and man like misprinted toys and trading cards. No lower legs beneath the knee means shorter means cuter?
So really it depends on if you are writing them obeying programming where they might shun damaged goods so the child buys a new Fluffy or it may slot into intentional glitches like hating knockoffs and seeing damaged Fluffies that way, or just incomplete programming tying their empathy to cuteness. Otherwise, animals and the cruelty of nature where the weak are shunned.
Or simplify it as a cheap trick to make kind Fluffies Hellgremliner. Establish villains or make them all trash.
In real life most wolf packs often continue to protect the crippled, and some species of ants care for their disabled while others shun or prey on them. You can back up anything you choose to do, if you treat them as living creatures rather than flesh robots.