It has happened to me on several occasions using older versions of the Cyclemeter app. Their support people told me that it was a GPS parsing issue that caused the app to stop. When you reached your final destination and noticed the app was stopped, starting it again would cause the GPS to turn back on and mark your current location. Since it didn't track you from the point where it stopped, it creates a straight line from that point to your current location. You may want to contact Strava support and explain what happened to you and send them a screen shot or site link of/to the ride. You may also want to make sure that you have the latest version of the software and also the latest version of any firmware for sensors you may be using. They can also cause the app to stop in mid ride. Hope this helps you out.
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HCFR Cycling Team
Ride Safe ... Ride Hard ... Ride Daily
2017 Colnago C-RS
2012 Colnago Ace
2010 Giant Cypress