Chatted with a volunteer today at an awareness event for the Cinnamon Trust.
She was telling me they need volunteers to long term foster cats (and dogs) of people who have died. Long term foster apparently means you foster the animal for the rest of its life. She was saying that the Cinamon Trust will pay all vet bills and that some of the animals have 'issues'.
Not fostering no. I was, for a long time, a volunteer dog walker and general driver for old people who needed to take their pet to a vet.
However their long term foster scheme is the same as ours (http://www.celiahammond.org/index.php?module=pagemaster&PAGE_user_op=view_page&PAGE_id=8&MMN_position=14:14) and appears to work in exactly the same way. Most of my cats could be considered to be long term fosters. Is there anything you aren't sure about or anything you have particular concerns about?
So OP. To answer your questions. Yes, the cat would be yours forever. Yes there are many, many cats needing long term fostering. It's very hard to rehome 'normally' old and/or ill cats, so often long term foster is the only way.
And yes, you would be expected to buy food etc yourself. It's only vet feesd that are covered.
Yes generally it will be just being old, or maybe having long term health conditions even if they're relatively young. Generally speaking they are the cats that people won't want to just adopt as they worry about racking up huge vet bills.
Not for the Cinnamon Trust but I have twice done long-term fostering of cats that had health problems, and were never to be offered for rehoming. The charity paid all vet bills, and in the case of the second cat they also paid for her food (special kidney support diet). With the first cat, who didn't have special dietary needs (she had mammary cancer) they gave me some food for her on a rather ad hoc basis but I bought most of it.
They were both 'mine' for life (cat 1 was with me for three years, cat 2 for two years) and the cost to me was very small. It is worth keeping in mind that choice of treatment would be down to the charity rather than you - eg there could come a point where the charity would opt to PTS rather than try expensive treatment with uncertain results or only likely to prolong life for a short while. Of course if you opted to pay for the treatment the charity would probably be fine with that.
I have fostered for a different charity since (though only short-term so far) and they have paid for all food and also litter, as well as any vet treatment. So there's a bit of variation in what's covered.