does car insurance cover run over animals?

Unless the pet owner could prove the incident was the drivers fault, or in part then no, The pet owner woudl also have to demonstrate that they had no liability.

ferinstance how was it that the animal was in a place to be hit by car.

it sounds to me like its the pet owner doesnt' have any or adequate insurance and is looking for someone else to pay,

The insurance should cover any third party loss which was the fault of the driver. If it's not the driver's fault (for example if the dog ran out in front of him) then he or his insurance company can't be expected to pay for any losses which the owner suffered. As you pointed out if the dog did any damage to the car then the driver could even claim against the owner.

Let's be honest, if an owner doesn't keep their pet secure and it gets loose and ends up in an RTC do you think it was likely to be caused purely by bad driving?

EDIT: Fairdo is quite correct that the animal is not the third party. In the event of a claim it is the owner who would be the third party since he is the one who suffered financial loss. Sorry if I didn't make that clear. None of this makes the idea of a successful claim any more likely though since the driver would have to be found to be a primary cause in the collision. Unless there were witnesses who saw him driving negligently and through this negligence cause the collision this just isn't going to happen.

No, an animal is not a 3rd party. The man whose pet was knocked down would have no claim on the motorist it is up to the pet owner to keep their pet under control, which includes not letting it run into the road and get run over. maybe the driver will come forward - then sue the pet owner for the cost of repairing the damage to his car.

As has been said, a dog CAN be controlled. So if a dog runs in front of you, gets knocked down and damages your car. The dogs owner is liable for the damage. Your not liable for the dead or injured dog. A cat on the other hand would be classed as a 50/50 case.

I've personally helped an injured dog with its owner to the vet without looking for a claim for damages to my car. The poor creature ended up being put down :(

Dogs can, or should be controlled. Cats are a law unto themselves.

No way to prove it was the drivers fault if a cat dashed across the road.

there's a stable risk that your coverage won't cover the robbery when you consider which you left the engine working. Leaving the engine working is in basic terms soliciting for it to be stolen. And as your license is suspended the coverage is often void while you're making use of it. With the two a sort of circumstances in play, it does not look stable which you will get something from the coverage corporation. Pray that the cops recuperate it and that it is not heavily broken while they do.

.. and exactly whose fault was it that their dog was on the road in the first place?