My dog was killed by a car while it was left fog dog care to another person? Can I ask for any damages due to negligence?

Yes, this sounds like a case of negligence in what we call a bailment - where someone was entrusted to hold and care for your property for you and you paid them to do that.  The problem is that all you can recover is the value of your dog and dogs are generally not worth much.  Unless it was a purebred, a service animal, or some other dog of specific value, most dogs are basically free.  The law does not recognize the sentimental value of your dog, although this is starting to change.  Who knows, maybe if you put it to a jury, they will agree with you that your dog is not worth nothing and they could award you some compensatory damages for your loss.  However, to prepare for and put on a jury trial takes a lot of work and you are unlikely to find a lawyer who would take this case on a contingency. This answer is given in accordance with the laws of Virginia and may not be applicable in any other state.  It should not be construed as legal advice, as that would require a more thorough analysis of all of the facts involved in a specific case.  If you need further information or assistance, please feel free to contact my office for a consultation. Case results depend upon a variety of factors unique to each case. Case results do not guarantee or predict a similar result in any future case.