In the late '60s my father had deposited his passport at the Polish embassy in London to get a visa. About two weeks later we were due to go to Brussels for a wedding. The embassy wouldn't/couldn't give his passport back. He phoned the passport office who told him to go to a room in Queens building at Heathrow. They typed his name on the front page (the one that starts "Her Britannic Majestey......) out of a passport (just the page) and sent him on his way. When we arrived at Brussels the border officer looked at it, shrugged, and let us through.
About 20 years later my mother was off to New York on her own. She presented her documents at T4 checkin to be told her passport was out of date - she'd picked up the wrong one (despite the cut corner). Luckily she only lived in Chiswick so when she phoned me I told her to get a taxi home, get him to wait and when she got back to T4 to grab the first BA person she saw, explain what happened and hope!. It worked although I'm not sure she enjoyed the experience as they rushed her through all the formalities!
My wife got pickpocketed as we walked out of Milan station. We phoned the embassy and they told us they couldn't do anything until Monday (this was Friday night). The passport was in a wallett that had some personal value so she decided to try and find in by looking in the rubbish bins outside the station. We were rummaging in a bin when an "urchin" came up and asked if we had lost "this" - the wallet. The money was gone but the passport was still there. He got a reward. I'm not sure the embassy believed the story when we told them!