Opposite of caregiver

Charge or ward might be appropriate to this meaning.

Patient implies that they have a medical condition that requires looking after. But, perhaps they merely have a generalized condition requiring constant care. If it is medically stable and doesn't need any acute treatment, it seems inapt to refer to them as a patient.

Whereas, it would be a perfectly legitimate catchall to say:

The caretaker spent his time watching over his charge.

This does not imply that their relationship is restricted to being medical in nature.

Charge is a person or thing committed to the care (meaning in the care) of another. (source at 3d)

Children is day care are called charges.

Dependent works whether the caregiver is paid, unpaid, related or unrelated to the disabled individual.

The care recipient or receiver of care or person in care seemed to get used in official language.

The cared-for perhaps.

In the BE version of the care sector, I've heard them called: Clients, Service Users, Residents (of a Care Home / Hospice), and even (occasionally) Caree.

Patients is still common in hospital settings, but not as a form of address where names are used to be assured of the correct treatment reaching it's target.