I'm using a dimension LE track (violin strings) and I recorded a track 4 beats long. The problem is that after the four beats, the track keeps playing the last note when it should stop making noise once the track reaches its end. Does anyone know how to fix this?

MIDI notes require both note ON and note OFF information. It is possible that you slip-editted the right edge of the clip and hid the note OFF portion. If you hover the mouse over the right edge of the MIDI clip until you see a ] cursor and click-drag that to the right, does that note then end?
 
Another alternative is to right click the MIDI clip in question and select "Bounce to Clip(s)."

It probably won't keep happening as you develop the project, but one work-around is to open "Event List" for that track, select the last note, press insert key (which duplicates the note), shift it forward to the beginning of the next bar, and set velocity 0.    Just in case it's a pedal (CC64) being stuck, you could also add a Controller 64 = 0 event.   Same way, select the last note, insert to duplicate it, select the "type" of note, use plus key or mouse to get the "kind of event" dialog, change to controller, set the field called "data" to 64 and the next field with no label to 0.