I've had similar problems as Drifter when leaving the fuel line attached to the outboard. Fuel sloshed out of the carb and washed down into the transom bracket bushings making a huge mess of gas, 2 stroke oil and grease. On my outboards I always disconnect the fuel line and run the engine out of fuel before loading up the boat.
On my I/O boat I don't, probably be pretty dangerous on that type of engine...
I disconnect my Johnson 6 when I dock, with the engine idling. The moment the idle starts to speed up, I hit the kill button. I've always done that to my outboards, with no ill effects whatever. I don't let them stop on their own, though. I catch it the instant it leans out at idle. Usually, I get my rear dock line tied before that happens.