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Here's a view of your original part (green) and box. I assume you want to make a cutout in the box to create a jig to hold the part for a machining operation.
If you subtract the box from the part you get the following unsatisfactory result.
If you make the box a little less tall and deep in the back the resulting Boolean subtract result becomes a little easier to deal with as shown here.
Exploding this shape and deleting surfaces that are above the bottom part surfaces yield the following. This is a surface model with holes by the red arrows. surfsculpt will not convert the surface model to a solid model unless the object is "watertight".
To plug these holes you can create a couple of cylinders, explode them and delete their tops as shown here.
YOu can now use surfsculpt to convert the surface model to a solid.
This may be sufficient to create the jig you need or you can modify the process.