A year after oil magnate Aubrey McClendondied in an auto crash, lawyers in Oklahoma City are sifting through the tangle of obligations and assets he left behind, trying to determine if he died a wealthy man—or swamped by debt.

As one of the biggest probate cases in history enters its second year, at stake is the resolution of more than $600 million of claims against Mr. McClendon’s estate that remain outstanding, according to court records and people familiar with the matter, out of a total exceeding $1.1 billion that were...