They don't make individual allowances really. Regardless of whether HB is paying the rent, part paying the rent or if they don't get HB. It doesn't consider individual expenses unless proved to be part of disability costs.
They just say income equals X amount, (and list the places where your income comes from eg which benefits, wages etc you receive).
The government says you need Y amount to live on (whatever the current fixed official figure is for basic expenses, looks like it's £189/wk from other posts) and carry out an income minus money-to-live-on calculation.
This is the extra you have left over (resulting figure from the above calculation). Your contribution towards care charges is Z amount per week (which may not be all of this left over figure).
What they don't do is say oooh bad luck you couldn't find a one bedroom property to rent or a property that's within the housing benefit amount, but never mind, we'll not charge you anything for your care because we can see you've got an extortionate rent to pay, or £5k debt on credit cards, or you're funding an adult DC/DGC through university etc etc etc. They're not interested in what your actual expenses are. It's a standard formula, a calculation, they follow.
The above concerns care in the community not residential care.
OP as the relatives, you will never have to pay for others care. Everyone pays for their own care. Otherwise the state steps in and pays. In theory. In reality it's quite usual to not be able to get the care one needs, despite the assessment. In those cases individuals or their relatives may choose to step in and provide care from their own pocket. It's worth noting that SS assess what care is needed based on "need" not want. If someone is paying privately for care or providing it for free themselves, that care is already meeting a need, therefore SS don't have to meet that same need. In other words, people often have to be left to suffer to establish that a need is present and can't be fulfilled another way.