You can use the write button. In the console view, activate the W button on the audio track for your strings. Then press play and drag the fader down to create the fade you want. When you're done Deselect the W button. Make sure the read (R) button is enabled. Now when you play it back, the fader should move exactly how you moved it when you were writing the automation. If it's not exactly what you want, just undo and try the process again. Hope that helps.

JaeSo it's really not as easy as making a fade in an audio track?

Sure, it's as easy as that.  Earlier, I just wanted to explain that software instruments need to be played and/or manipulated with MIDI in order to come to life.  Just triggering notes without working with the notes doesn't make for the most natural results.
 
But CC1 or CC11 is simple to use though - just - play it, or draw it in.  But as Leadfoot explains, you can automate the audio track down to zero and get the results you want.  It's not as if you Have to fade the strings to zero with MIDI.  Just using the quick fade tool right there on the clip is the fastest way - well, that tool is available on an audio track if you bounce your MIDI tracks to audio.
 
EDIT:  This may be the easiest thing for you if you want to do volume control on a MIDI clip.  In the track header/inspector, click the Edit Filer of one of your strings tracks, choose 11-Expression.  A yellow line will appear.  Add nodes and bring that down to zero.  That way you can get at the control without having to work in the PRV if you're not comfortable working there yet.
 
NOTE - It occurs to me that part of the confusion could be because you're using the "Simple Instrument" track which has both MIDI and Audio on the same track.  MIDI newcomers are often confused by that set up because it obscures what's going on.  I always recommend people try the old school way of having a separate MIDI track and associated Audio track for each instrument in a project.  That way, the user can clearly see what's going on.
 
I do have the impression that you need to get up to speed on some more basics and all this will be much simpler.
 
Randy B.

Freeze the track - turn it into audio (there is a single button that will do that).  Then you can add a volume envelope, which you need to learn about anyway.
 
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AT
Freeze the track - turn it into audio (there is a single button that will do that).  Then you can add a volume envelope...

Why freeze it?  Just add a volume envelope.