으면서 마치다

close the show with a song

All four lines here are the same broadcast sign-off: the host names a song and ends with 들으면서 마치겠습니다 or 들으면서 마칠게요, 'we'll finish while listening to this'. -(으)면서 sets the listening alongside the ending, and 마치다 is the formal word for wrapping something up. For casually finishing something you would hear 끝내다 instead.

Register: radio and broadcast sign-off, formal-polite