How do you ask a neighbor to control their wandering cat? I had this problem nearly forty years ago, and told the neighbor I was concerned about the safety of his pet. I'd seen his huge cat inside the tall cedar fence I'd built around my family yard where my dog was chained. The cat owner was rather arrogant when he answered. perhaps too arrogant for me to take lightly. He laughed and said no one dog alive could ever hurt that big cat of his!
That made me wonder at his lack of curiosity as to why I had built such a tall, expensive fence around my dog, then sometimes chained him with a solid link chain. It was not to protect him, I assure you. "Duke" was out of Alaskan Indian sled dog stock, and he had been bred, born, and raised 160 miles from the nearest paved road or street light. His sire must have been part Saint Bernard, judging by the width, weight, and strength of his and all of his five puppies heads, shoulders, and bodies.
I had sent Duke home, and my parents graciously went out of their way to accommodate the imposition of a six month old, 100 pound puppy when he arrived. Perhaps they understood what a large part that puppy had played in my own healing and coping process in having returned from the Republic of South Vietnam to the United States, then being sent to a remote site in Alaska for a year of what we sometimes called solitary confinement or lock down.
It seems to me I mentioned my conversation with the neighbor to my Dad, who had never had much use for cats (cats kill wild game). I forget if it was before or after the incident that occurred, it may have been both. Dad had seemed to like the dog, or at least respected him, and certainly had spared no expense or effort on building him a large stout kennel, one Duke had immediately escaped from. Dad had repaired it, but Duke was not comfortable in it until I came home and told him to "stay." After that Duke would stay in his six foot kennel, if not chained, until I called him from the front yard, then he'd jump it, then the shorter fence on the side yard. He'd come and sit beside me, ready for whatever adventure I had planned for my time off from work.
Oh, what happened to the monster cat? Well, it seems the only thing I'd ever seen Duke afraid of was a humongous wolverine we'd encountered in Alaska when he was just a pup, and anyone with a lick of sense knows to get out of Dodge when a wolverine comes after you! That damned arrogant cat never had a chance.