Short answer: No.
Long answer: Not as far as was can tell.
Black Holes (BHs) are solutions to the equations of General Relativity (GR) and GR is a phenomenally accurate and mathematically elegant theory of gravity. It shows that gravity is not a force at all, but a side-effect of the curvature of space-time. GR has been tested repeatedly and passed every test with flying colors. No other theory of gravity is as elegant or matches experiment better than GR. For those reasons, we think that GR gives a good picture of what's really going on with space, time and gravity.
A Black Hole is a region of space-time where mass-energy has been so concentrated and the curvature become so extreme that space-time inside the surface of the BH is fundamentally different than outside. Specifically, (and inevitably approximately since I'm using English and not math) space and time twist around so that inside the BH the radial coordinate is timelike. And that means that, just like outside the BH we can't stop ourselves from moving forward in time, inside the BH, we can't stop ourselves from falling towards the center.
Anything put inside the BH (inside its Event Horizon) inevitably, no matter what velocity it is moving at and no matter what kinds of acceleration is undergoes, falls to the center and is obliterated by the singularity that lurks there. In particular, unobtanium does not work if it is made of either matter or energy or a mixture of the two.
Assuming that Hawking Radiation exists (we have never observed it, but it's on pretty firm theoretical ground), all BHs eventually evaporate, but not before anything that crossed the Event Horizon has gone splat (or whatever) against the singularity and been destroyed.
Now we have some pretty good reasons for thinking that GR isn't the final theory of space-time and gravity, but those reasons also tell us that it is a very good approximation in big BHs and away from the central singularity. (Called the "weak field" region, though it's only weak by mathematical standards.) We also have good reason to think that whatever replaces the singularity in the New and Improved (and so-far Undiscovered) theory will be just as dangerous to matter and energy.
About the only way you can put something into a BH and get it back later is to either (a) ignore General Relativity altogether (in which case what's a Black Hole doing there?) or (b) assume that the super-scientists who discovered unobtanium have an arbitrary new theory which allows the construction of arbitrary new gadgets which do arbitrary things. (Either way you're using something called "magic".)