Guitar players?

Obviously the string didn’t play itself. And the guitar didn’t make a decision to play that string on its own. I was suggesting that after playing the same song over and over, it  SEEMS like my guitar knows the song well enough to do so. 

If you fretted a new note and missed picking the string, it could sound as a "hammer on", or just switch to the new pitch if that string was already sounding.

Not sure what you mean but that could be a resonance.

Every solid object has its characteristic frequency of vibration called fundamental frequency. When exposed to soundwave having that exact frequency, the object will start vibrating by itself.

For example, on properly tuned acoustic guitar if you have 2nd string tuned to B and if you play E on 5th fret of that string, the first, open E string will start ringing by itself because it picks the resonant frequency from its neighbor.

If not, then it's probably out od tune and you can pluck E on 2nd then turn the first peg with your right hand, still holding E on 2nd with your left until you can hear (and actually see) 1st empty string vibrating.

Edit:

String resonance can also be a consequence of harmonics (overtones). For example, an A string at 440 Hz will cause an E string at 330 Hz to resonate, because they share a common harmonics of 1320 Hz. Occurence of resonance from harmonics is characteristic for some stringed instruments like koto and vintage fender jazzmaster.