When the organisms die, they stop incorporating new C-14, and the old C-14 starts to decay back into N-14 by emitting beta particles.
For object over 4,000 years old the method becomes very unreliable for the following reason: Objects older then 4,000 years run into a problem in that there are few if any known artifacts to be used as the standard.
Despite this she continually uses the c14 dates to create 'absolute' chronologies.
She says this is ok so long as you take into account the correction factors from dendrochronology.
Libby, the discoverer of the C14 dating method, was very disappointed with this problem.
He understood that archaeological artifacts were readily available.