If you keep asking for more money, the Hinox will give you increasing amounts of rupees: First 5 when you approach him, then 20, then 50, then 100. If you ask for more rupees after all that, he will attack, enraged at your greed and trying to get back his rupees (that is by killing you. You do not lose rupees if he hurts you.) He will then attack you each time you enter his cavern. He seems to be invincible and touching him will deal 7 hearts of damage with the green tunic, even if you use your shield.
If you choose to stop asking for more money before he enrages, he will stay docile and not attack. If you talk to him, he will ask you to keep the bribery a "secret to everybody" and will not offer you any more money.
Either way, when you save and quit the game, his attitude will revert back to being scared and he will start the whole sequence over again, offering more rupees for his life.