(Preface: I've never tried to plug a set of WPs into any FMS that were going to require the sort of flightpath we're talking about here. With that said, here's what I believe having spent a little time on a few sims and way too much time looking at FMC/S documentation.)
The AP won't shut down at that point. If you're that close to the waypoint that you are going to require a very large direction change to reach it, then it would likely consider that waypoint as being overflown and activate the next one.
I've been doing a little bit of reading on the 777-200's FMS today. I've just learned that when out of waypoints, the AP will hold the last heading.
I've also heard a bit of speculation regarding the search area 1500nm off Perth. 40.7140° S, 85.6494° E roughly. When you change the 'S' to an 'N', you end up with a coordinate somewhere in Xinjiang province. Read into that what you will. Grasping at straws, or hijacking fumbled by a typo.
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