When a hopper is directed into a chest, it will not output items into the chest if it is both full and being fed the same items by another hopper.

In the image, when Hopper A is trying to feed items (ex. Coal) into a full Hopper B, then Hopper B will not feed items into the chest.

This has been tested with a Brewing Stand (using Nether Warts) and a Trapped Chest in place of the chest.

(Also, I did not find any similar issues through the search)