This is devastating for his family.
It is vital to clarify the legislation here. Despite what people say it is NOT LEGAL for a farmer to shoot a dog, whether or not it is worrying livestock.
The legislation states that if a dog is worrying stock then the LEGAL option is to seize the dog and bring it to the guards / the guards can seize the dog.
The legislation states that if you ILLEGALLY shoot a dog then you can use the fact that the dog was worrying livestock as part of your defence.
However, the life of the livestock is equally as important as the dog, and if the dog is in fact a danger to the livestock and the farmer cannot safely seize the dog then I can see why they may see no option other than shooting the dog.
Perhaps a solution here may be rubber bullets for farmers?
The only solution is responsible ownership, not letting your dog off leash around livestock, ensuring your dog is secure and cannot escape (particularly if living near livestock) and, if you think your dog may be around livestock then it is VITAL to work on DESENSITISATION EXERCISES so that your dog has no desire to chase the livestock.
This video may help with teaching your dog to ignore livestock.
My thoughts go out to Finn's family.