In every gun I can think of that has one, the extractor is holding on to the cartridge when it is in the chamber. On many guns the extractor engages long before the cartridge is fully seated.
If it did not engage the cartridge before it was fired, how would you be able to remove the cartridge without firing it?
Are you possibly getting the extractor confused with the ejector?
When the bolt is closed and a round is chambered, the extractor (which is usually a hook shaped thingy attached to the bolt or slide) is stuck in the extractor groove of the cartridge case. When the bolt moves backwards the hook pulls the cartridge case out of the chamber. When the bolt gets far enough back the ejector kicks it off the extractor hook and out the ejection port. The ejector can be either just a piece of steel that the moving bolt/slide pulls the cartridge back onto, or it can be a spring-loaded plunger that, when the bolt/slide gets to a certain spot, trips the spring and the plunger comes forward and kicks the cartridge out.
Meddle not in the affairs of dragons, for thou art crunchy, and taste good with catsup - George of Lod, Year of Our Lord 297
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