I know the kind of neighbors you mean. You could feel them out a bit in conversation over the fence, without indicating you may need to take action. If they are kind of overwhelmed or lackadaisical, then you know you are going to have to do something because they can't or won't. Least "in your face" way is to get a small animal live trap, set it where it's not in their field of vision, bait it with tuna, catch cat, carry to animal shelter. (cover cage when moving). Or you can call animal control, but that will possibly cause bad, or hard feelings, or retaliation. If you have someone with a chip on their shoulder or mental/personality issues you need to be as clandestine as possible ......