Tāmen de shìchǎng fèné bèi jìngzhēng duìshǒu cánshí.
Their market share was gradually eroded by competitors.
Tips
memory
蚕 means silkworm, 食 means to eat. Imagine a silkworm slowly eating through mulberry leaves — that steady, methodical nibbling is exactly what 蚕食 describes when territory or resources are gradually eaten away.