Answer by taking a quote from the following article:

Henry Hill, Jr. was born on June 11, 1943 in Manhattan, New York, to Henry Hill, Sr., an Irish immigrant and electrician, and Carmela Costa Hill, a Sicilian. The working-class family consisted of Henry and his eight siblings who grew up in Brownsville, a poorer area of the East New York section of Brooklyn. From an early age, Hill admired the local mobsters who socialized across the street from his home, including Paul Vario, a capo in the Lucchese crime family. In 1955, when Hill was 11 years old, he wandered into the cabstand across the street looking for a part-time after-school job.

On April 27, 1980, Hill was arrested on a narcotics-trafficking charge. He became convinced that his former associates planned to have him killed: Vario, for dealing drugs; and Burke, to prevent Hill from implicating him in the Lufthansa Heist. Hill heard on a wiretap that his associates Angelo Sepe and Anthony Stabile were anxious to have him killed, and that they were telling Burke that Hill "is no good", and that he "is a junkie". Burke told them "not to worry about it". Hill was more convinced by a surveillance tape played to him by federal investigators, in which Burke tells Vario of their need to have Hill "whacked." But Hill still wouldn't talk to the investigators. While in his cell, the officers would tell Hill that the prosecutor, Ed McDonald, wanted to speak with him, and Hill would yell: "Fuck you and McDonald". Hill became even more paranoid because he thought Burke had officers on the inside and would have him killed.  While Karen was worried, she kept getting calls from Jimmy Burke's wife, Mickey, asking when Hill was coming home, or if Karen needed anything. Hill knew the calls were prompted by Jimmy.  When Hill was finally released on bail, he met Burke at a restaurant they always went to. Burke told Hill that they should meet at a bar Hill had never heard of or seen before, owned by "Charlie the Jap". However, Hill never met Burke there; instead they met at Burke's sweatshop with Karen and asked for the address in Florida where Hill was to kill Bobby Germaine's son with Anthony Stabile. Hill knew he was going to get killed in Florida, but he needed to stay on the streets to make money.  McDonald didn't want to take any chances and arrested Hill as a material witness in the Lufthansa robbery. Hill then agreed to become an informant and signed an agreement with the United States Department of Justice Organized Crime Strike Force on May 27, 1980. In 2011, former junior mob associate Greg Bucceroni alleged that, after Hill's 1980 arrest, Jimmy Burke offered him money to arrange a meeting between Bucceroni and Hill at a Brooklyn grocery store so that Burke could have Hill murdered gangland fashion, but Bucceroni decided quietly against having any involvement with the hit on Hill. Shortly afterwards, Burke and several other Lucchese crime family members were arrested by federal authorities.

What happened that kept Hill from being murdered?
Shortly afterwards, Burke and several other Lucchese crime family members were arrested by federal authorities.