It's an 1871 Rolling Block action chambered in Winchester 38-55 caliber, correct? But it is an original Remington 1871 Rolling block, or an original Springfield Armory 1871 Rolling Block (Remington patent), or is it one of the modern replicas of the Remington 1871 Rolling Block in 38-55 Winchester, made by Uberti, Pedersoli, etc.
The only Winchester rifle with the numbers "71" in its name, that I am aware of in 38-55 caliber, is the Model 71 lever action, it came out in 1935.
Pictures and serial number would help with the appraisal, if they are available.
Yup, that a trap door springfield in those photos, and if chambered for the .38-55 should not be fired with anything but carefully loaded , mild ,black powder loads, as the chamber pressure for a .38-55 with a full charge of black powder is 30,000 CUP, while the trap door action when new was only good for 25,000 CUP, and in an original gun today, most gunsmiths with experience with this action will tell you to keep it below 18,000 CUP to be on the safe side. And never fire them with smokeless powder loads.
I suspect this gun has been rebarreled with the barrel from some Winchester rifle, for to the best of my knowledge Winchester never made a Trap Door, and all the original guns were chambered for the 45-70, although rebarreling to other cartridges after they left the Springfield factory was/is pretty common, but was usually for cartrdges in t h e .40-.50 caliber range.
Mbogo is pretty close to right, it's a wall hanger or parts donor, you might get as much as $50 piecemeal for the parts, based on what I can see in the pictures and the OP's comments on the state of the action, stock, etc.