Okay, so the name may not be considered very PC today – you could also call this a cross-dominant stock. The concept was to allow a shooter to mount the gun in one shoulder but sight with their opposite eye. This was useful for cross-dominant shooters (ie, right handed but left eyed) or shooters who had suffered a crippling injury to one hand or one eye.
The craftsmanship involved in properly making such a gun is quite impressive. The frame and tang are made with a slight curve to them, and then the stock must be made paying careful attention to the direction of the wood grain, so that it can withstand the bending moment created when firing. A fantastic piece of work, and something generally restricted to the rather wealthy.
For non-native English speakers using the word "cripple" can be considered as a very offensive way to refer to someone with a disability or handicap. Please don't call people that.
Just like people can be right or left handed people have a dominant eye. Shooters use this eye from aiming. For most people that will match their dominant hand, but a few are cross dominant (ex. Right handed but left eye dominant).
Being cross dominant makes shooting awkward because they're forced to choose to shoot with their dominant hand or dominant eye. This bent design would allow a right handed shooter to aim with their left dominant eye.
Yep, cross dominant here and it's so fucking annoying. Growing up took me a while to figure out, couldn't understand why I wanted to play lefty in hockey and lacrosse despite my right hand dominance in everything else. Shooting instructor in scout camp was the one who figured out I was left eye dominant and all of a sudden I was a much better shot than before.