Had a similar occurrence on my Fatboy with stator going south. I was on my way to dealer and bike cut off on me, and I had to jump it to get it back started. I thought this was really odd since I keep it plugged up to a Battery Tender at all times when it's not being ridden. After restarting bike I was on the interstate and I noticed the speedometer stopped working, lights stopped working, and finally the bike quit again. Had to call the dealer and have them pick me up on the side of the road.
Along with the parts you mentioned my battery went tits up within thirty days of them replacing stator, so you may want to keep an eye on that also. What happened in my case I believe is when the stator went south and wasn't charging the battery anymore I was running on battery until it went dead and that damaged battery.
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Ride Safe,
Fired00d
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