My DSis currently has a swollen bandaged hand and is on antibiotics. She adopted a cat a few months ago. Molly is eight or nine years old and has had at least two previous homes. The rescue centre warned that she was known to "nip", but I'd say that she bites, as she breaks the skin. She's very shy and rarely goes outside as she's frightened of other cats. She spends a lot of her time in her favourite hiding places in DSis's house, but maybe twice a day she will come out and be sociable.
Approximately 29 times out of 30 there's no problem - Molly will approach someone and nuzzle them, sometimes even climbing on to their lap. She appears to be asking to be stroked and we learned pretty quickly that she likes to be stroked on the top of her head and never under the chin. Nevertheless, she sometimes bites hard and with little or no warning. She has bitten DSis, BIL and me (although the second time she tried to bite me, I managed to snatch my hand away just in time). She doesn't show any obvious signs of having had enough of being stroked, e.g. pulling away, miaowing or thumping her tail.
DSis worries that at her age, she'll never learn not to bite. I don't know why she does it - is it anger or could she be over-excited or even trying to play?