Sometimes a retained placenta happens after delivery by chance, when some of the placenta passes out and some remains. It happened to my sister and the doctors didn't notice it. She was hospitalized for an infection one week after giving birth. That's when they found the remaining placenta and removed it. And she had to take IV antibiotics. It was kind of traumatizing for her because she wanted to be with her newborn and not at the hospital.
I've even heard that sometimes this can happen with a c-section, the doctor can miss a part of the placenta.
These are all rare incidents though. Thankfully, it doesn't happen to most people.