If a structure were sufficiently strong at a large enough radius from a black hole, could it completely enclose a black hole without collapsing in, since in some sense the material would pull on itself uniformly?
The structure you are describing sounds similar to a Dyson sphere, which has been proposed as a method of extracting energy from a star by an extremely advanced civilisation. For distances much larger than the Schwarzschild radius, a black hole has the same gravitational field as a star of the same mass, so the same physics applies*. It is theoretically possible, but well beyond the realms of current materials science and engineering.
One problem with constructing such a structure is that it is unstable: small perturbations would cause it to drift off until the central mass collided with the wall. This is precisely because of the effect you mention: the gravitational forces cancel out leaving no net force on the shell (this is known as the shell theorem).
*Thanks to D. Halsey for suggesting this clarification.