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Subverted: The Baby is in the road about to get run over by a car. Alice goes out running into the road, pushes the baby out of the way, leaving her open to get run over by the car, but the car stops and neither Alice or Baby are hurt.
Double Subverted: Then another car comes from the other direction and hits Alice. Baby is still fine.
Babies are everywhere around the city, narrowly escaping various dangers while their teenage babysitters, Funny Animal pets, crooked kidnappers, and other guardians are getting pummeled.
Alternatively, all of the babysitter figures mentioned above have meetings to discuss the perils they go through because of the infants they're protecting.
Zig Zagged: Baby goes exploring the city, with Alice following him the whole time. Along the way, both Alice and Baby are pummeled and beaten nearly equally as they try to escape the very dangerous landscape.
Averted: Baby and Alice stay home the whole night, and nothing goes wrong.
Enforced: "We have a Butt Monkey main character and a ridiculously cute baby character. Let's put them in an hilarious cartoon together and make sure the child doesn't get hurt. Parents hate to see that."
Lampshaded: "Does every baby sitter have to deal with these problems? Am I doing something wrong?"
Invoked: Baby is actually incredibly evil and sadistic and loves seeing Alice in pain. So he goes out into the most dangerous places, knowing that Infant Immortality will protect him.
Exploited: Alice tells Bob to take care of Baby. Alice doesn't like Bob much.
Defied: Alice locks all the doors and windows and puts Baby in a nice secure crib to keep him from escaping and getting into trouble.
Discussed: "There goes Alice chasing Baby into the construction site again. This can't end well for her."
Conversed: "What a careless baby sitter. What kind of person just lets their infant go into dangerous spots like that? He's getting exactly what's coming to him."
After repeatedly getting injured while babysitting, Alice is mentally traumatised and has to enter therapy.
The baby is an Enfant Terrible who deliberately sets up these scenarios either out of raw malice towards the babysitter(s) or as part of a plan to ensure that nobody would want to babysit him meaning that his parents have to stay home/spend time with him.
Alice gets herself killed, and the baby becomes orphaned.
Reconstructed: A terrible accident is about to incur but Alice managed to save the Baby in time, and while Alice got injured in the process she is viewed as a heroine for saving the Baby.