And is this SoftTouch hardware?
Yes - - Type 4 drop-out trigger. No serial would usually mean it was not factory fitted to a gun. But the partial serials on stocks are worthless anyway. Some inventory stocks are numbered according to the Perazzi dimension list.Based on the wider cut out on the bottom vs narrower top tang, cutouts on both sides for the locking bar, and relieved area on the inside of the left side (as we see it), It looks like a removable trigger stock for a newer O/U (MX8 or similar.