Im using version 1.7.2 stable
I noticed that if you make a Big barrel of any wood type or sign type then break the sign the barrel still persist but its not a big deal because it go away after you break any block thats apart of the structure.

Heres video of it happening on my server
https://www.youtube.com/watch?v=TvVs0QDgP2I&feature=youtu.be

For some reason this do not effect the small barrels

This is intended behavior.

Big barrels main block is actually the front fence. Removing that will destroy the barrel.
This is intended so players can make the Barrels look a bit nicer without the sign on top.
I know this is confusing as the small barrels need the sign, but i thought it is still nice to allow the sign to be removeable on the big barrels.