I'm interested in this subject for educational purposes. I myself was unable to get such software. The only applications I was able to find are these for manual modelling, but these don't interest me.
However, I found two papers with interesting solutions:
 "Torus Figure Generating System Based on Graph Theoretical Representation and Topological Analysis"
This one is fine. You provide a flat figure as input, and you get 2-D multi-bar impossible object in output.
However, neither software, nor source code provided; neither authors were kind enough to share such on my request. And the algorithm is not clearly providen to get something useful from it
 "Computer-Aided Creation of Impossible Objects and Impossible Motions"
Not bad, but very brief. You have an impossible object projection at input, and you end with a possible 3-D object which gives that projection from some point of view.
It's unclear how to compute the end figure
So if one knows where to find the software of my interest, please mail me: firstname.lastname@example.org The source code is a must.
P.S.: I'm not interested in cheap tricks like "just disable z-buffer and mess up the sorting order, and voilá, you have that object" 
 <a href="http://www.jstage.jst.go.jp/article/jsoft/20/4/20_4_625/_article">http://www.jstage.jst.go.jp/article/jsoft/20/4/20_ 4_625/_article</a>
 <a href="http://www.keisu.t.u-tokyo.ac.jp/research/techrep/data/2007/METR07-41.pdf">http://www.keisu.t.u-tokyo.ac.jp/research/techrep/ data/2007/METR07-41.pdf</a>
 <a href="http://gamedev.stackexchange.com/questions/56230/is-the-impossible-object-possible-in-computer-graphics">http://gamedev.stackexchange.com/questions/56230/i s-the-impossible-object-possible-in-computer-graphi cs</a>