Noticed this a few times now. When villager or soldier is killed in battle (animal or raider) they sometimes get grave injured status and need to be carried to doctor.
Well when this happens they often times continue with their work anyways. I just had trader still carry around stone to trade center. Also if it happens i can command them to move as any other villager.
But i also seen soldiers that fell in battle chase retreating raiders. Sometimes it looks funny but pretty sure its not supposed to happen.
Echoing similar issue:
When non general laborers (miner, herber, etc) are injured and need to go to the clinic/hospital to heal, they will not go/cannot be transported unless they are removed from their profession. Instead they will idle until they either die or are manually removed from their labor assignment. Upon being removed from the labor assigned, they will route to the clinic but stay in the laying down position instead of getting up - essentially sliding into the clinic.