“The Poor Itch,” the unfinished, final play of playwright John Belluso, will receive a full production at the Public Theater this and next week following a lengthy series of workshops. Belluso, who was confined to a wheelchair, was only 36 when he died last year and was widely considered a rising talent in the theater world. He wrote passionately about characters with disabilities. A mix of dreamscape and reality, “The Poor Itch” centers on a 22-year-old veteran of the war in Iraq who lost the use of his legs and now suffers from Post-Traumatic Stress Disorder and a dependence on pain killers. While Belluso did in fact write several complete drafts of the play, it was not technically finished. The current production is described as a mix of several different versions of the play.