Ideally, you don't share passwords. If it is a server, every user should have their own account with sudo access if needed.

If it is a website that you are unable to add multiple users to an organization with, LastPass has a password sharing feature that doesn't directly expose the password with people you share it with. Although if someone cares enough, they will be able to find it.

Any time an employee leaves a company, all shared passwords should be reset. It doesn't matter if it was an amicable departure or not.