Yes and no.
Nobody’s ability to pay charges affects whether or not they get care, under the Care Act. One’s contractual consent is not necessary – one is obliged to pay by the Care Act, once the charge is levied, but on the other hand, NOT paying does not mean that the council can stop putting the care IN.
However, anyone with more than £23250 in savings that are not required to be disregarded, should not be getting subsidised financially FOR their care, BY the council.
If they need care in a care home, the council will not organise their care for them, and pay for it upfront, normally, unless the person lacks capacity to contract in their own name and no-one else is authorised or willing.
On the other hand, if they need care at home, they are still entitled to a care plan and services from the council. And since the council may well pay less than a private person would, so getting one’s services through the council may mean that one ultimately gets more for less out of one’s own personal financial resources.