MAKIYIVKA, Ukraine—Fighting may have ebbed in eastern Ukraine, but one thing is becoming clear in this separatist-controlled mining town: The economic ties with Kiev still bind.

Eighteen miners at one of the main coal enterprises here died fighting for Russian-backed forces who carved out a tiny quasi-state last year. But it still needs Ukraine to buy its product, provide head lamps and safety equipment, and process wages through its banking system.

“We...