A reaping was a Lyran ritual of distributing captured prisoners of war. County-level reapings were organized when large amounts of prisoners were taken. (Star Trek: The Stoneship Files: "The Defector")
The Count could select four prisoners in advance. Then, by order of seniority at the highest rank, other flag officers could select as many prisoners as the number of stars in their rank, i.e. a vice admiral could select three prisoners, a senior commodore could select two and a commodore could select one) and later have everyone select, in order of seniority, one prisoner.
If a flag officer was demoted, it would have no impact on their reaping status. However, once a prisoner is selected, its new "owner" could do anything with the prisoner, after notifying Lyran Starfleet Command. With her reaping ticket, Brianna Reiss thus sent Alaa to give conferences at universities on Malachor V. (Star Trek: The Stoneship Files: "The Defector")