What goes wrong
A retry loop that calls a paid API every second. A voice agent that never hangs up on a silent line. A scraper that hits your site and triggers your chatbot ten thousand times. All real, all common, all invisible until the invoice.
Warnings do not work
Budget alerts arrive by email after the fact. Providers process them hourly at best. By the time you read it, the damage is done.
What a hard cap is
A counter per service per day. When it reaches the number you set, the service stops for the rest of the day and a message goes to you with the reason. The cap cannot be exceeded by a busy day or by a bug, because the counter is checked before every paid call.
Setting the number
Take a normal busy day, double it, that is the cap. For a small office that is often 400 call minutes, 2,000 email operations, 300 chats. When the cap hits on a genuinely busy day, you raise it with one message. That is a good problem.
Where AI Office applies it
Phone minutes, model calls, text messages, document pages, chat conversations. Each has its own cap, each shows in the morning digest next to what it produced.