This is the 630th most frequent Korean word.
마친
The Korean word "마친" means "finished" or "completed."
The word "마친" here refers to the action "to finish" and functions as an attributive verb form describing the noun "후에" (after).
그는 보고서를 마친 후에 휴식을 취했다.
He took a rest after finishing the report.
Here, "마친" describes the state of completion of the class in conjunction with "상태였다" (was the state).
수업이 이미 마친 상태였다.
The class had already been completed.
In this sentence, "마친" functions to describe "일이" (work) as having been finished in the conditional phrase.