Many of us remember the 2103 Tour de France where a small dog was in the path of a 100 bike peleton motoring at nearly 50 mph. Fortunately, no one crashed. Marcus Burghardt wasn’t so lucky in 2007 when he collided with a dog in 2007.
The owner of an animal is responsible for injuries caused by an animal running loose. Most cities have leash laws and require owners to fence or control their animals. Unincorporated areas typically have no such restrictions. An owner can still be responsible. Animal identification is criticial and a cell phone or witnesses may be necessary.
I have handled a cat/bike incident. The offending cat liked to pounce on bike rolling bike wheels, believe it or not. The owner even admitted it! A crash occurred. The cyclist was injured. A homeowners policy paid for damages. Early investigation and identification turned the tide.