In my headcanon Kolyat was on duty with C-Sec when the Coup happened, and he was with Bailey when Shep found him, so he tagged along with Shep and squad and interferred with his Dad's fight with Kai, and distracted the bastard long enough for Shepard to go help Thane, and after a long protracted, actually awesome fight, they kill beat Kai off. The rest goes on as it does now, but only with Thane alive, and HAVING THE LUNG TRANSPLANT, YOU STUPID DRELL!!!
My Head cannon is that my shepard got in between Thane and kai ding-a-ling and biotically punched her fist into kai's chest pulled out his dark souless heart and ate it while the bastard fell dead!....okay well she didn't eat it but she threw it at Thane and told him to never charge forward into a sword again,then she jumped on top of him and kissed him and told him how much she loves him!
In my head cannon Thane is already cured he was just watching out for his Siha!