
Notch-jaw pliers have a simple but effective modification to aid gripping. The cuts in the jaw grip from above, locking on to the corners of external drive heads and dig notches into the circular shape of gouged internal drive heads. You even have a chance with a sheared shaft as long as it's bigger than the notch.
Vampliers® (fangs for extracting that screw...)

Locking Pliers with Unique Non-Slip/gripping Screw Removal Jaws for The Easy Extraction of Damaged/Stuck Screws, Black/Green. Neji-Saurus mole Grip Pliers by...
4.0

Screw Removal/gripping Pliers (Combi Style) with Unique Non-Slip Jaws for Quickly extracting Damaged Screws (Green Grips). Made in Japan. ENGINEER pz-58 GT...
5.0
Neji-saurus® (Neji is Japanese for Screw)

ENGINEER PZ-66 Screw Removal Locking Pliers Screw Saurus VP-3 Vice Saurus
4.0

Screw Removal/gripping Pliers with Unique Non-Slip Jaws for Quickly extracting Damaged Screws. Made in Japan. ENGINEER pz-55 neji-Saurus
4.0