As others have noted, once you get on the losing path (if you hit Proxima, you're going to fail no matter how well you fly), you fight at Sol till you either eject or get killed.
If you eject, you're taken aboard Thrak's dreadnaught, and brought before him. He gives you the chance to beg for mercy, at which point you have 2 choices: one is admit defeat, and generally acting like someone who's will to live was taken away, after which the guards blast you from behind; the other option is defiance, in the previously mentioned "screw you" scene, and Thrak guts you like he did Angel.
As for dueling with Thrak after the Behemoth is destroyed, while it is possible to kill him and get back to the carrier at the time (they're on a countdown to get out of Loki after the B's destruction), it's not exactly easy. In the original DOS version, if you salvo-fire all your missiles at him, then afterburn back to the Victory, generally he winds up dead (especially so if you let loose with all 8 missiles in an Arrow), and you can make it with roughly 15-20 seconds to spare, depending on what fighter you're in. If you're playing the Kilrathi Saga version of WC3, though the Vic jumps as soon as Thrak dies (even if there's time remaining), leaving you stranded, and bringing your advancement in the game to a dead halt.
Even if you do destroy Thrakhath and land on the Victory before it jumps out, though, you still face him again over Kilrah, as if nothing had happened in Loki.
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SubCrid Death
Official Net.Nazi,
LOAF's Merry Guild