You are liable for all damage done by your dog - regardless of what you think of the bill. That doesn't mean the dog's owner will recover the full amount - a judge or jury will determine what is reasonable - but what you think is reasonable is irrelevant. You are also liable for the replacement value of the dog. The law is changing as to sentimental value, etc, so it's impossible to say what your full liability might be.
If you have homeowner's or renter's insurance, turn the claim over to it. You may want to speak with a local attorney. The State Bar of California can give you a referral: www.calbar.ca.gov
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
By your own admission, your dog escaped. While out, it attacked and inflicted fatal wounds on someone else's dog. While there may well be extenuating circumstances regarding the location of the other animal and its actions, you are likely responsible for all costs the other dog's owner incurred as the result of the attack, plus the replacement value of the dog.
While there seems to be some movement regarding sentimental value/emotional distress, at this point CA seems to follow the standard rule of treating pets as inert property.
If you can settle prior to court, it is probably in your interest to do so. However, if you "have no money," you would seem to be coming to the table empty-handed.
If you have renters or homeowners insurance, you should have already notified your carrier.
The foregoing is for general information purposes and does not establish an attorney-client relationship.
You woudl be liable for reasonable vert bills. However, under the facts that yu stated, you would not be liable for sentimental value, punitive damages or emotional distress.