I changed the tag from Personal Injury to one about Animals.
If I am reading correctly,you have lost your pet to an attack and you suspect the neighbor's pet, but were not present for any attack. Someone working on a fence may or may not have any relationship to what took place with your pet.
I am sorry for your loss, but there is very little information here.
I am sorry this happened to you. While there "may" have been no witnesses there is circumstantial evidence that the neighbors dog killed your dog. Circumstantial evidence is "good" evidence often the best kind. If they have homeowners coverage that coverage should pay the claim. If not you can make a claim in small claims court. Regretfully most states consider a pet merely personal property; like a lamp. If someone damages your lamp, they are responsible for the repairs and if no repairs are possible then the value of a similar lamp, same age, etc. The value of the claim would be the value of the dog at the time it was killed.
If you feel this is the "best" answer or is "helpful," please indicate. Since I am limited to the information you provide, I cannot guarantee the accuracy of the answer. You should seek the advise of an attorney who can explore all aspects of your question. This communication does not form an attorney client relationship.
I'm so sorry to hear about your dog's death. The following Avvo guide should contain some helpful information for you. Best of luck.