MASYAF, Syria—Officials told Ghadeera Malouk that her son, a 28-year-old medic in the Syrian army, died during a mission in the rebel-held suburbs of eastern Damascus. In the days after, Mrs. Malouk held a memorial and secured a gravesite here in the family’s hometown.

Then the army called again. There was no body. Her son, they said, wasn’t dead—he was missing. That was more than two years ago.

Now,...