Every scenario is different and the wind conditions and kite size would influence the most which decision to take in case one or both front line breaks.
I never had a single front line break, but about 3-4 times when the depower rope snapped, essentially releasing both front lines at the same time and leaving you with both back lines pulling hard. The most recent one was about 2 months ago in 30 knots. The fact that I had a 5m kite made this rescue possible as pulling one of your BACK lines in those conditions is very tricky. I essentially did the exact same thing mentioned by Puetz. It was very difficult to get to the kite a there was a huge amount of tension on the back line. I eventually self-rescued by sailing in.
Kites aren't meant to be flagged out on back lines, it can cause erratic behavior of the kite such as the kite spinning around the wing tip in a continuous loop, scary suff, I had this happen before on a old Cabrinha bar flagging to a single back line. Also, in strong winds, wrapping a back line around the bar would be extremely difficult due to the amount of pull....however, in light to moderate winds, it wouldn't be such a big deal.
If your kite starts to death loop which would be a possible outcome if a single front line breaks then releasing your kite completely would be a good option if you are in strong/very strong winds. Have a look at the video below, jump to time: 5:10.
In such off-shore conditions there is typically much lower winds at the surface of the water, hence why in this case he could flag the kite safely.
Again, every scenario is different what happens in the video when he cuts the lines could really vary in other conditions or with other kites/sizes.
Christian