Directors have an obligation to act in the best interests of all shareholders. Certain things will probably be overlooked (small related party loans to the majority shareholder etc) but if say the majority shareholder sells his struggling private company at a vastly inflated price to the public company then the directors who approve the deal open themselves up to legal action by shareholders.
Example: Company ABC has $100m in cash. Mr X is majority shareholder and wants the $100m for himself rather than sharing it around as a dividend. He decides to sell his private company XYZ to ABC at a vastly inflated price so he can take the $100m. The directors in this instance have the obligation to ABC to ensure that the purchase is in the best interests of all ABC shareholders not just Mr X.
It's a pretty fine line, yes the opportunity exists but it really is not that easy.
Always look out for any related party transactions. These are always disclosed in the notes.
A majority shareholder by definition has more than 50% of the shares on issue. They control the board.