It all depends on the boat design. For our boat, I first tried just tacking and leaving the jib as is (partially furled for the 25-30 knots we were in). The boat immediately fell off downwind and gybed. Next attempt was with about half as much jib, with the same result. Finally, tried jib fully furled and it worked fine--once headway was lost and keel stalled, boat would round up to 20 degrees from the wind and stay there.
You need to try the experiment with your own boat.