Job offer likelihood to rescind?

Hello!! First corporate job and my onboarding is December 15th. I just completed all their medical testing and whatnot as it is for a healthcare position. I haven’t given my current job my 2 weeks yet in fear the new employer may rescind my employment before I start on the 15th. I accepted their job offer as well and passed any drug screenings, but this a thing? Just looking to quell some of my anxiety!! Sorry if this has been asked before.