After Sabin "won" the coin toss, he decided to keep an eye on Figaro. He trained in martial arts assuming (correctly) that one day he would be needed by Edgar and his Kingdom. A man named Duncan took Sabin under his wing as an apprentice, training both him and his own son, Vargas.
Duncan saw a lot of potential in Sabin and taught him almost everything he knew, most importantly his blitzes. Vargas must have not been as dedicated, or well, dedicated to the wrong things, because he wasn't taught his father's blitzes. Sabin said it was because Vargas was so hungry for power. Anyway, Sabin was far more advanced, and was taught more by Duncan, so it's easy to see that Duncan may have favored Sabin. If he didn't favor Sabin, Vargas might have easily thought that, all the same. Vargas assumed Duncan was going to make Sabin his successor, and he grew so mad with jealousy that he killed his own father, at least in his own mind.
When you're scaling Mt. Koltz with Locke, Terra, and Edgar, you'll eventually run into Vargas. Having just offed his father, and looking to kill Sabin, he was at Mt. Koltz looking for Sabin. He runs into the party instead, and attacks them. Fighting him looks like a lost cause, but Sabin comes to save the day.
Sabin apparently thought that Duncan was killed too, and he confronts Vargas about it. He doesn't understand why Vargas thought that Sabin was going to be Duncan's successor.
Our Master wanted you to be his successor, not me. He appreciated your fine spirit.
You'll need to use Sabin's blitzes that Duncan taught him to defeat Vargas, and Vargas will be surprised that Sabin knows Duncan's blitzes. He will take off after being defeated. I'm not really sure what happens to Vargas after you beat him, as he's not seen in the remainder of the game. I assume he lives the rest of his life in regret, if not madness for what he did to his father over a poor assumption.
Later on in the game, you can come across Duncan's house where Sabin will find out Duncan is alive, and Duncan will teach Sabin his last and best blitz, Bum Rush. Sabin grows teary seeing Duncan, so it's obvious that Duncan meant something to him in those ten years he trained after leaving Figaro. Having just lost his father when he met Duncan, Duncan likely became a father figure to him. I think Vargas may have just attacked his father and left him for dead, thinking he wouldn't survive. He obviously did survive, and it's nice that Sabin gets to see him again. So all ends well in that "freedom" stage of Sabin's life.
I think it's interesting to note that even though Sabin chose "freedom", he was never really free. The responsibility of Figaro was always heavy on him, and he trained close to Figaro so that he could watch his Kingdom, knowing that he would eventually be needed. Starting a new life without Figaro was just a dream Sabin momentarily had on the night of the coin toss. The fact is that Sabin, like Edgar, would always feel responsible for Figaro and never be free of it.