Number one thing is the float needle that sets the fuel height in the bowl is probably leaking, not cutting off completely. All it takes between the needle and the seat is a hair and it will leak.
The seat the needle sits up into can also leak between it and the carb body. Some bikes have a copper washer and some have a rubber O ring to seal between the seat and carb body but either can start to leak.
That's the most common, but if the fuel tank gets a blocked breather they can pressurise and force fuel through anyway.
If you normally turn your fuel tap off it should prevent the problem, but if it isn't then your tap might be leaking slightly as well. You can test the tap by pulling the hose off the carb and turning it up so fuel's filling the end of it with the tap off, then watch the fuel level in the hose for a minute. if it looks like it comes up, then blow gently or wipe the excess fuel away and watch again.
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