Bear,
What you have is a No. 40 New Model Pocket rifle with a 10" barrel (the 2" octagonal breech is part of it). It is fitted with the optional Stevens "combined" sights. Yes, it should have a wire butt stock that fits on the back of the grip. Made between 1902-1912. the serial number will give a good idea of when it was made and which frame style it is.