For example, one of the reasons why the North American raccoon has established itself in Central and Southern Europe was partly due to it being kept in private collections as a pet (along of course with fur farms).
Pretty much entirely fur farms I believe - with little to no input from escapee pets..... which is one reason it's frankly ridiculous they are now banned in zoos and private collections within Europe, but fur farms retain an exemption
there are also believed to be small populations living in the wild.
There were in any case - the coati breeding population in Cumbria (a zoo escape) died off around 2010 after about a decade, when a harsh winter killed off the last stragglers. Ironically there have only really been big problems with feral individuals of the species since the ban - much as occurred with other species, there have been cases of animals being dumped in the wild.