At the end, the FBI is seemingly satisfied that the shapeshifter is dead and everyone is accounted for. However, they only found one body, the nurse's. To close the investigation, they would need to find two bodies: the dead nurse, and the shapeshifter disguised as the nurse. Even using the incinerator, the shapeshifter couldn't have disposed of the nurse's body without a trace. So there's no reason why the FBI should close the case.