The ‘how they work’ aspect is quite well set-out here:
Pros & Cons of Care Fee Annuities - Care Fees Annuity (care-fees-annuity.co.uk)
Obviously, the annuity aspect is only one of several elements which fall to be considered in such unfortunate circumstances, and there is never an optimal decision/path in these matters, as many of the decision-making factors will be subjective/uncertain and one needs to keep an eye on what tomorrow may bring.