For as far back as people can remember, they've been there in boardrooms across Japan, the lingering ghosts of past regimes.

They are the former presidents and executives who stick around for years in adviser roles after their stint at the top has finished. Old men — usually — with no legal responsibility but plenty of power, they've long been criticized for getting in the way of incumbent management teams.

Suddenly, their presence is being questioned anew as the nation overhauls its corporate governance structures. The trade ministry — credited with masterminding the high-growth era until the 1980s — has started an investigation. An influential proxy adviser plans to urge clients to vote against company attempts to introduce the system, and the man tasked with suggesting what's next for Japan's firms says it's time advisers stepped down.