Interesting, I recently spoke with someone from a fishing cat conservation group in India and he told me the same thing, and that the government will pay you for your livestock if a fishing cat (or other rare species) killed it. Is that true? He was very confused when I was telling him how we deal with livestock and mountain lion conflicts.
It's a little different here with these types of encounters (foxes, raccoons, mink, weasels, etc.). They are very abundant in North America, so when there is a "conflict" with livestock or pets, it is easier and cheaper to kill that animal than catch it and relocate it. That one fox family being killed doesn't affect the total population at all really, so it's just removing the problem animal. That's most of the scenarios.
Sometimes there are animals that kill livestock but you are not allowed to kill them yourself (hawks, bears, fisher, ravens, etc.), and then we would call our natural resources management office. Depending on the classification of the animal, they would either give you permission to kill it yourself, go kill it for you, or do what you said and relocate the animal.
That's a really simplified version, but you probably get the point.
Oh I get this