usually these die sets are 4 pce ,and are sharpened specially as set of four , quite often in jobbing shops you use the worn out,broken ,remaing peices [as what is in your picture] for some of the following,thread chasing, single point threading, ground to make full form profile tool, radius form both concave and convex, [as parent material is hss ,most reuse the peices and regrind to suit applicable task for one offs{might be for 100 plus items done as one off job}than purchase a new peice of hss [expense] and grind profiles into that peice.
some turners make holders with suitable clamping section to hold altered alfred herbert die piece that they then hold in capstan or revolving toolpost,
hope this explains why you only have bits and peices of die sets , and why some have been reground/repurposed
cheers rob