Going back to the original question, they very occassionally turn up in rescues. Being held onto by some rescues who think that everyone else would exploit the pigs in question. Sadly due to the inflated prices some are exploited that's true but one thing rescue work has taught me is that ALL pigs are at risk of exploitation and some of the places I have seen many many hairy pigs are exploited for money and kept in overcrowded filthy conditions with inadequate food and no medical treatment given for conditions. I have only ever witnesses one exploitation of skinnies which was no where near as bad as the hairy ones I have been in - but it still wasnt right.
I think you would be very unlikely to find one in a rescue.
As for inbreeding - again I have seen so many inbred pigs and been in many situations where 2 hairy pigs have become 60, totally inbred pigs. I have one here who is a complete mess having been inbred to get certain ears and nose for showing - a hairy pig who has suffered her whole life.
As guinea pig gaga has stated the majority of skinny pigs being bred around the UK are strong, NOT inbred and the breed has moved on hugely from the genetic mess it was when they first came about - I for one am grateful for that.