Nope-I was taught not to shoot anything I don’t intend to eat...
Not only Florida has this problem-I’m guessing that any rural area where snowbirds winter has abandoned pets wandering around with frayed collars, becoming fast food for predators and feral dogs. And putting down a pet you are tired of isn’t the act of a decent human being, any more than turning them out into the wild is-people like that should never have a pet, other than a rock.
It has been my observation that winter people/snowbirds treat the properties they rent for the season even worse than they treat the seasonal pets-mostly, the rent they paid for the season is barely enough to cover the damages incurred to said property.
Many ice houses and businesses with cabins and RV spaces have signs asking that people who do not want a pet any more bring it to one of the several no-kill animal rescue centers nearby, and lists their addresses and phone numbers. Two of my three cats are former RV/snowbird cats from a local shelter-both are happy, healthy pets now, but one of them was starving and injured when brought in, and neither would have survived much longer in the woods.