Good advice, Paul.
That F Pack should either be preceded by a dose of sorbate or the F Pack itself should include sorbate. (Many instructions for making an F Pack say to use sorbate.) The K-Meta doesn't so much kill the yeast as it does shock them and slows them down considerably. Adding K-Meta and sorbate is the "stabilization" step that follows fermentation.
The K-Meta slows the yeast down, so they are not very much in the "mood" to eat anymore; the sorbate then prevents those yeast from multiplying anymore.
As a result, when the current generation of yeast dies, there should be no future generation to take their place to continue converting sugar to alcohol and CO2. So, when new sugar is added (from the F pack), the yeast can no longer process it.
Needless to say, if sorbate is not added to sterilize the yeast, then more sugar is added, and the existing yeast recover from the shock of the K-Meta dose, fermentation will start again and continue until either the sugar is once again all gone or the alcohol level gets so high that it kills the yeast.
Sorbate is not so critical for wine if it is not going to be back-sweetened. In this situation, many of us just never add the sorbate. However, if you are not going to bulk age your wine, but bottle it right away, I would always add the sorbate as directed.