As per the book, Gaspipe...

When Fat Pete was recuperating in the hospital, the Lucchese's sent a hit man, dressed as a doctor to finish the job. He worked with a real nurse, who got him to within a couple of feet of Fat Pete. The FBI agents were ready for this and arrested the hit man.

Casso/Amuso sent word to Fat Pete that his elderly parents would be whacked if he flipped. Neither Casso/Amuso took responsibility for this cardinal sin, each one blaming the other for ordering the hit against a family member. So, Pete's parents, wife and children were quickly put in the witness protection program.

That left his sister...