Final answer:
The most likely issue when a shell casing is not extracted from a firearm's chamber is a failure to extract. This indicates a malfunction in the firearm's extraction mechanism.
Step-by-step explanation:
When the spent shell casing is not extracted from the chamber of a weapon, the most likely issue is failure to extract. This problem occurs when the mechanism of the firearm that is designed to remove the spent casing from the chamber after firing does not function properly. The other options listed, such as double feed, failure to eject, and failure to fire, describe different issues: a double feed is when two rounds are fed into the chamber at the same time, failure to eject is when the casing is extracted but not ejected from the firearm, and failure to fire is when the firearm fails to discharge a round.
For example, if the extractor, which is responsible for gripping the rim of the casing and pulling it out, is worn out or damaged, it may fail to properly extract the casing. Similarly, if there is debris or fouling in the chamber, it can prevent the casing from being extracted.
In contrast, the other options mentioned in the question refer to different issues: double feed is when two rounds are fed into the chamber simultaneously, failure to eject is when the spent casing is not ejected from the weapon after firing, and failure to fire is when the round does not ignite upon pulling the trigger.