I just defeated the Wither boss in survival. Right after that I stopped playing. When I reloaded the world, the wither came back. So I had 2 Nether Stars from 1 Wither. I decided to test some stuff in creative if it was possible to dupe Nether Stars. I found out that it was possible. Right after the Wither dies and drops the star and before the health bar is gone, I went into my inventory and exited the screen in my inventory. I came back and the same wither had more health and the star was lying on the ground. It didn't always drop the star, but most of the times it did.

Technically should work in Survival