It is a misconception that cats abandon sick kittens. Domestic cats generally do not abandon their kittens, even if they are ill.
Why Cats Stay
Maternal instinct: Mothers are dedicated to protecting and caring for their young.
Survival: Kittens depend on the mother, so she is unlikely to leave them.
Nurturing: She will lick, clean, and warm sick kittens.
Exceptions
A mother might struggle if she is overwhelmed, stressed, or dealing with a contagious illness. If a kitten is truly abandoned or seriously ill, seek veterinary care immediately or contact a rescue organization.
In most cases, leave the mother to care for her kittens unless neglect is evident.