Edward Nelson passed away at age 82 on September 10, 2014. You can read a tribute to Nelson's illustrious career from Princeton University.
Although he worked on the inconsistency of PA until the end, there were no standing claims to a proof of the inconsistency of PA at the time of Nelson's unfortunate passing.
On September 30, 2015, Nelson's unfinished manuscriptmanuscripts titled Inconsistency of Primitive Recursive Arithmetic hasand Elements have been posted on the arXiv, with a foreword by Sarah Jones Nelson and an afterword by Sam Buss and Terry Tao.