No, first of all, there is no crime of "accidental injury to death" in the criminal law, but there is a crime of negligent death, but the crime of negligent death refers to the behavior that the actor thinks that he can avoid the death of others and deprive others of their right to life because he did not foresee it or has foreseen it.
In this case, B slipped because the floor under his feet was slippery, and the fruit knife was inserted into A's chest, which was an accident and did not constitute the crime of negligent death. The accident did not require criminal responsibility.