1. In general, a stepchild who was not adopted by his stepparent cannot inherit if that stepparent dies without a will.
2. There are some exceptions. Those exceptions generally require that there be clear and compelling evidence that the stepparent intended to adopt the stepchild, but was unable to do so due to some legal obstacle (normally, the opposition of the parent whom the stepparent isn't married to).
3. Children over the age of 12 cannot be adopted without their consent.

Which means: a stepchild who refused to be adopted can legally inherit from their dead stepparent, so long as there is clear and convincing evidence that the stepparent would have adopted the child if the child had allowed it.

Bizarre.