Failing the task but fulfilling the intent

In Burning Wheel we become well practiced at describing a successful task but failing the the intent. What does the opposite look like in play?

To search the room for Queen Anne’s secret communications with her brother, Philip IV.
Your task is that you start opening drawers. Intent, to find the letter without making a disturbance or being caught. To fail with a successful task is to find a hidden compartment in a drawer in Anne’s desk as Mme Combalet enters the room.

The example given in the book for failed task and fulfilled intent is:

*Due to a bad seal, you inhale some vapors of mercury during the operation. You have a crushing headache for 1d6 days and suffer a -1 to all rolls for the duration.” The player creates the recipe they were after, but at a cost to themself.

It looks like success with a condition without saying as much. Ruined gear, suffering relationships, loss of status. It’s that sort of thing, isn’t it?