yeok jigwoni bunsilmuri deureoomyeon baro yeonrakhae jugessdago haesseoyo.

Because there are really two clauses here:

• 역 직원이 = the station employee is the subject of the main clause
• 분실물이 들어오면 = if a lost item comes in / is turned in, where 분실물 is the subject of the conditional clause

So each clause can have its own subject:

• main clause subject: 역 직원이
• subordinate clause subject: 분실물이

This is completely normal in Korean.

분실물 means lost property, a lost item, or something that has been lost.

It is a common word you will see in places like stations, airports, schools, and public offices.

Related words:

• 분실 = loss, losing something
• 물 = thing, item

So 분실물 is literally something like a lost thing/item.