One of the men, Bomani Africa, 61, has admitted to killing Mr. Galdieri; he is scheduled to be sentenced June 7.
The second man, George J. Bratsenis, who has not been charged, appeared on Feb. 22 in federal court in Newark in connection to the case. But the proceeding was abruptly adjourned, and neither prosecutors nor Mr. Bratsenis’s lawyer would say why.
Mr. Bratsenis, 73, and James Caddle, who died in 2016, were housed in the same prison in Newark for three years, from January 2007 to April 2010, state records show, but it is unclear if their paths would have crossed.
The prominence of Mr. Caddle’s lawyer — Edwin J. Jacobs Jr., well known for representing clients tied to organized crime — fed into initial speculation that the stakes in the case were high.
Then, days after Mr. Caddle’s plea, Mark D. Sheridan, a son of Joyce and John Sheridan, who were stabbed and burned in their home near Princeton, N.J., asked prosecutors to reopen their case. He also asked that a knife found in Mr. Bratsenis’s truck be tested for DNA, adding a fresh layer of intrigue.
Mr. Sheridan, a confidante to several governors, was a Republican leader and onetime state transportation commissioner who was running one of the region’s largest health care networks when he died.
Mr. Jacobs said he had been representing Mr. Caddle since at least 2019, when Mr. Caddle got a subpoena from state investigators. Officials with the school district in Elizabeth, N.J., where Mr. Caddle did campaign work, confirmed that they had been ordered to turn over thousands of documents at about the same time.