The better queston is what will happen to Ukraine. PLC will survive anyway, although Polish-Lithuanian nobels will push for reconquest for Ukraine (or Ruthenia, as it was called at the time). Hell, it might even get them to make some reforms strengthening royal power to fight more effectively.
And Ukraine would have become a target of her neighbours. I'm simply not sure if she was capable to remain independent for long. From west she would have been hard pressed by Poles; from east by Russians and Khanate of Crimea, which would need a place to be raided. My guess is? Sooner or later it would hase been divided between Poland and Russia or incorporated into Russia, as IOTL.