State laws can differ so to find out if the owner of the dog would be held liable for the damages a person sustained due hitting an un-collared dog that ran into the roadway, check with a lawyer familiar with you state's liability laws.
Some states with negligence laws may find the motorist partly at fault if they hit the dog instead of the other way around where the dog strikes the vehicle and is at fault. To figure out your consumer rights and if the dog owner can be held totally responsible in your particular situation, try getting legal advice or perhaps try contacting your state's insurance regulator.