If making a selection is marking the first included frame and the first non-included frame (which is the very right way to do), then the video display should end with a dummy frame which is the one to mark to select the whole video. Else, whatever trickery is used to do without that frame is warping reality and not getting the right frame count. I bet that source code would get straighter this way.
To prevent user astonishment, the dummy frame can indicate something like "THE END - This picture is not part of the video but is the one to mark for a selection up to the end".