Hi, seems to be correct, also noted here
I had a similar story in this card from a teenager: here
This could be one of the explanations if the person was assigned to work, but there could be other reasons as well.
p. 366 just example for sending people back to Auschwitz
206 prisoners were sent back to Auschwitz II- Birkenau. Since the factory was only interested in those fi t to work and those who possessed a healthy capacity for labor, these women were sent to the extermination camp