Had half an 80 mm screw (5mm diameter) break off level with the surface
of mortar between bricks yesterday. It was held in by a plastic wallplug.

Having wondered about using a screw remover, drilling it out, and
several other suggestions on the internet, I thought about using heat. I
have a soldering head for a gas-powered blow lamp, so heated that up and
applied it to the end of the screw for a few minutes. After a while I
pushed some narrow-nosed pliers into the soft plastic on either side of
the screw and was able to grip it and turn the screw a little. After
repeating this a few times the screw was out enough to grip it properly
.. After about 15 mm was out, I was able to pull it out with the remains
of the plug.

Maybe this has already been suggested, and of course it would be of less
use with a screw in a heat-sensitive surface. But it might prove useful
if other methods fail.

--

Jeff