Open the MP3 file in two different media players to verify that the file itself is corrupted. For instance, if your main player is iTunes, try opening the file in Quicktime, Windows Media Player or even your web browser. Proceed to the following step if the song cuts off early in both players. If it does not cut off early in the alternate player, the problem is in your main player's settings. Select the track in the player's window and look for a setting called "Stop Time" (in iTunes it's in File->Get Info->Options). Deselect that check box.
Download and install the free sound editing program Audacity (see Resources). While you cannot restore the ending of the corrupted file, you can minimize the impact of the abrupt ending on the listener.
Open the file in Audacity. When you see the sound wave appear, hold down your cursor to select the full last 5 seconds or so.
Click on the "Effect" menu. From the list that drops down, select "Fade Out."
Save the file as an MP3. While you have not restored any missing data, which is impossible short of downloading a new file, the song will now end more smoothly in any media player.