There are a few things to be said about inbreeding.
The first is that linebreeding is inbreeding deliberately engaged in by the breeder to establish an "abnormal" or new variety. Examples might be breeding sheep to get finer wool, or aviculturalists establishing another colour mutation. The wise breeder then returns to the "normal" population to reintroduce genetic variation once he/she has established the variety.
Inbreeding itself may or may not introduce reproductive problems that may or may not lead to the extinction of the population. There are plenty of inbred island species, for instance, while many dassyurid species are inbred because they go through boom-bust cycles. In effect it is a crap shoot. But of course reproductive problems are not the only medical problems that can become endemic in an inbred population, and there are plenty of domestic animals that could be used as examples of that.
The conservation problem with inbreeding is that it reduces genetic diversity, and so when it comes to reintroducing a species they may not have the genetic diversity within the population to adapt to varied conditions.
There maybe nothing at all wrong with inbred animals. All it really means is that they belong to a population that all have common ancestors and therefore very similar genetic makeup. Take an inbred animal and mate it to an animal that it is not related to (even if that animal belongs to another inbred population) and you have progeny that is not inbred.
Inbreeding is something that should be avoided in wild animal populations, but sometimes there is no choice. Sometimes a decision has to be made to deal with what you have got.