This is a fascinating question because Willie Cicci's character was reportedly based on the real-life mobster Joe Valachi, the first Mafia member to publicly acknowledge the Mafia's existence.
In 1963, Valachi testified to the congressional committee about how the mafia actually worked, providing intimate details of its history, operations and aiding in the solution of several unsolved murders.
After speaking to the committee, he was reportedly guarded by up to 200 US Marshals due to a rumored $100,000 bounty on his head. He spent the rest of his life in protective custody in prison and died, with the bounty uncollected.
It was partly due to his testimony and protection that the US actually created the Witness Protection Program (in 1970).
Therefore, it seems entirely plausible that Cicci's character in the films was based on Valachi and that he would have entered custodial protection scheme as Valachi did.
What really happens to him in the film is a mystery. We are never told. Given Michael has Fredo murdered, it seems highly unlikely he would not make an attempt on Cicci's life. Whether that attempt would be successful or not is unknown.
On a side-note, there are many sites online that claim Cicci was supposed to return in The Godfather III, but his character was cut after the actor portraying him, Joe Spinell, passed away. I can't find any official confirmation that this was the case though.