Yes your sketch is still sending out serial data, however if there is no program in the PC attached to the com port then there will be no data being sent to the PC, this is a function of the arduino on-board USB serial converter chip and the PC's USB driver supporting the arduino board, and it's that chip that controls the send and receive leds, not the avr chip running your sketch.
So reopen the serial monitor and it will reset the board, restarting the sketch and the serial send led will run for as long as you have the serial monitor opened, close it and the serial send led should stop.
That make sense?
Lefty