Since my apprenticeship days ,we always used to catch hold of longer rods as they were parted off,it was shop practice,and as we were making instrument parts and damage to the part was frowned on as it meant more polishing,later on ,damage to the employee was not thought about,small parts were caught in a tobacco tin which had a few holes in the bottom to drain the slurry. Fifty years later I still do it on long parts,small parts with holes are caught on a screwdriver or land on the swarf between the bed ways which acts as a cushion.Parting off in those days was all high speed toolbits laboriously ground to shape but they worked better as they had more side clearance,speed was usually half normal turning speed, All apprentices did their 6 month turn on the Ward capstan, sometimes parting off a couple of thousand parts a week,for the first hour or so in winter the slurry was freezing cold,and it rotted our shoes,One thing do not hold hexagon bar when parting off ,if your hand is near the tool post it really hurts.Keep the tool blade as short as possible,non working slides locked,speed lower,on the capstan parting tools were usually on the front and form tools to the rear,and don't break the blade when the turret is fed forward,On the Boxford parting off was done from the front (no rear tool post) and with four way tool post,which is better for holding tools rigid but nowadays prefer the Dixon tool holders as it makes turning so much easier, particularly on one offs ,at work batches were up to 200 hundred so the time to shim up the tools in the four way was lost. One other comment is if the job is to be sawed off after parting most of the way then remove the rod from the lathe and saw it off in the vice.