An example (for US law) might be the Anthrax Poisoning, which a lot folks no doubt remember. The FBI announced they believed their main suspect was the person responsible. The suspect was also dead. That's the FBI's opinion, not any kind of court finding, but it was pretty important in terms of taking a public position on a major case that hit the country while still in the throes of shock from 9/11.
AFAIK, police investigators can re-visit any investigation at any time, closed or not. Or they can decline to. If there's an investigator on this board, feel free to contradict me, but I'd assume any number of variables might come into play, public scrutiny, work load, interest by politicians or victims' advocates, new evidence (a biggie I'd think), the results of appeals, an investigator's own discretion, etc.
I once met a NYPD cop who worked cold cases, including some that were pretty well in permafrost. He said at one point the cold case squad looked into some evidence relating to the Judge Crater disappearance, which had gone cold about seventy years before.