Along the lines of kids being just dropped off at church nurseries and the parent disappearing, I had the following happen one year at Vacation Bible School. I was the registrar and we were handling the massive influx of parents to register and fill out paperwork. Some people were pre-registered, and the registration form clearly stated to let us know if your child has an allergy.
2 kids are just hanging around the area outside the sanctuary where we are doing registration. After awhile, they ask for a particular person. Said person is supposed to be taking care of them but I haven't seen the person all morning. It turns out that she was there but just hadn't come upstairs yet. I know her, and knew she was supposed to be there, but not that she was actually there or that she was supposed to be taking care of these kids. Oh, and the boy tells me that the person is also supposed to have their snacks in the kitchen, which puzzles me until I ask him and find out the real details.
It turns out that Mom literally dropped off a 7 year old brother and 5 year old sister for VBS and drove away. She had talked to the person that they knew, and the person agreed to watch out for them, get them registered, etc. And this person was also supposed to bring in their peanut-allergy safe snacks. Which the person had done, but no one talked to anyone about it. As far as we knew there were no kids registered with peanut or other allergies. The person left the snacks in the kitchen, but they weren't marked for these particular kids. So the volunteers preparing snacks had no idea why the snacks were there and who they were for, so they could have just been tossed and the kids fed the regular snack which was not guaranteed to be allergen-free.
So 2 SS for the price of one - a Mom who has kids with allergies (peanuts for the brother and it turns out dairy for the sister) who just drops them off without connecting up with anyone and seeing that her kids would be safe, and the person she was supposed to connect with, who didn't bother to let anyone know that she was responsible for them. The chuch leaders didn't like it when I threated to call the police the next year if this happened again. The next year I was not asked to be registrar.