Similar things apply in car insurance... only items common to the use of the vehicle AS a vehicle (Sub woofer permanently installed, cd player/stereo, speakers, GPS NOT on your Cell phone) are covered if somebody breaks in OR you are liable/responsible for the accident (did damage to yourself/your own items). If somebody breaks into your car or you wreck your car and your pets are injured, your car insurance will not pay for their damages/injuries. Pets, unless pet specific insurance exists and is purchaced for them under their own policy, a car insurance policy, will typically regard your pets no different as they would your purse/credit card/laptop you thought was well enough hidden under your seat: as items not covered under your car policy. They might be items covered under home-owners, but as already mentioned, pets are a different thing entirely.
Just some things to keep in mind regarding insurance and your pets (and personal belongings). Read your home/car insurance policy and understand it.