I guess I'll pose a scenario: a man robbs a bank at gunpoint. The prosecuter(state) takes the accused to trial and finds him guilty of armed robbery, decides not to charge him with possession of a firearm. Could the state charge him at a later point with possession?
To use a (tragically) real world example:
Donny shoots and kills three adults and their small child. As he leaves in his truck, he's pulled over for speeding. He shoots and kills the officer.
Donny is only charged with the death of the officer. He's convicted and actually does get executed, but is never charged with the other deaths. The State can indeed charge him at their leisure..or they could have before the execution.
The State generally has a pretty good reason for using this tactic. You'll figure it out.