Everything will be Ok as long as the CVX dividend is paid. Management is irrelevant. Large CVX institutional investors like Vanguard own over half the stock and don't care if the company is going into the toilet as long as they get their dividend. They will flip the stock quickly when the lack of finding oil, and reduced income cant support the dividend. The Chevron stock price will implode as the institutional investors dump the stock.
@as+1jsyerxty said it well.