You may hold the dog owner personally liable for their injuries. In this situation, the at-fault party must pay for damages from their pocket or through their assets. It includes savings, properties, etc.
You may also involve other parties who were negligent during the incident. Suppose the dog owner rents the property where the incident occurred. In that case, you may name the landlord as a defendant in your dog bite injury claim.
In such cases, consulting with your dog bite lawyer before negotiating with other parties is essential.