This article may contain spoilers.
This dilemma can occur when you're at the university (can be random)
On the far right side the following choices can be displayed:
1. Let them take it
2. Destroy it
If you happen to have a infected survivor, he will demand the vaccine and allowing the infected survivor to take it can result in him getting cured or dying, if nobody is infected nothing will happen or one of your survivor(s) might still have a chance of dying.
Nothing happens, but relationships can get affected.