If you have something on the house, it is given to you free by a business:
All the drinks were on the house.
(from Cambridge Advanced Learner's Dictionary)
If it hasn't vanished yet, it's probably still there
Hungarian folk tales often start with the phrase: "What follows may or may not be true."
Thus a story unfolds. And at the end, the story might refer to a character by saying: "If he is not dead, he may be living still," according to a collection of Hungarian folk tales, published by Iwanami Shoten, Publishers. The stories are very heartwarming.
One is about three housewives drinking in an inn. They tell the innkeeper they have decided that whoever among them can't manage to fool her husband will pay the tab.
All three go home, play tricks on their husbands and return to the inn.
As they all have fooled their husbands, the innkeeper says, "All right, the drinks are on the house." ...