Hmm. That's different. Because in that case I wouldn't expect a constant influx. Most modern pet breed lines are traced back to a small group of imported animals that have in recent years been carefully bred out to avoid (more) incest and add desired attributes (cf: the history of non-traditionally-coloured Siamese cats). I'd expect a small pool to start off with and then near-constant inbreeding.

I'm referencing the case of Siamese cats in Britain, and I think that's a good place to start looking, because here we have a small population in an isolated area that could not pull in new blood, that was actively encouraged to expand. Halfbreed cats were common but never permitted to enter the breeding pools. The problems were noted and breeders did try to minimise them, so we have a record of the problems incest produces and the strategies practiced to prevent them. I think it's worth looking at.