I can't imagine a situation in which that would make sense. By virtue of sending messages back that weren't flagging that you were compromised, it would be assumed that you were still disguised.

The exact opposite is pretty much done, though much more subtly. When British spies were infiltrating Europe during the second world war, they would send encrypted messages back to their handlers. In every one of those messages, they would make a deliberate error (Like, misspell STOP as STEP) to signal that the person operating the radio was the spy, and that he wasn't compromised. They would then omit the error, or the germans who captured their books and radio would simply not know the flag, which would tell the handlers that the spy was captured.

Maybe not exactly what you are looking for, but there is a good first hand account of the CIA rep at the US embassy in Tehran describing his time in captivity after the Islamic Revolution (although it wasn't written at the time of his captivity). Although they obviously knew he was a member of the US government, initially his captors were not aware of his ties to the CIA (though they later figured that out after reconstructing some shredded documents). I found it to be a really interesting read.

A First Tour Like No Other, by William J. Daugherty