Not sure if it's only specific abilities, but I've had my dachshund (w/ herd ability) indoors for a while, and recently made it my furmiliar, and it actually still comes out of my house and herds my animals.Since the Furmiliar lives within your farm house, the pet will no longer do its pet abilities.
Furmiliar section in SOS: ToT guide
I noticed that on the Furmiliar page, Gifts section, it mentions: