Victims rescued from the Athi Rivers complex last September revealed they had signed contracts with an unnamed overseas employment agency, committing to pay up to $18,000 (£13,000) for visas, travel, accommodation, and other logistics, the police said.
Oscar Jenkins, a 32-year-old teacher, was captured last year while fighting for Ukraine.
It comes after two were attacked and another raided by Israeli forces in the past few days.
Ukrainian volunteers are going house to house in Pokrovsk as Russian drones hunt from the skies.