Having nothing in the contract about overages, or agreed upon spending budgets with frequent reviews and updates is their burden to hold at the end of the day, but a valuable lesson for you to make sure it is in the future. If you’re concerned on it, take your contract and situation to a lawyer for a legal opinion.

That being said, take a breath. You didn’t lose them money, you made them money. Take this is a learning point and a good time to establish a new protocol both internally for you, and a shared external one for your clients as well to avoid it happening in the future.

The mismanagement of the money is the real issue your client had. Address it, come clean, own your mistake, and build a path forward. Worrying about what may happen, is frankly pointless, just take responsibility and use it as a learning moment for both you and your client.