It's pretty normal, when you take a carb apart. To find fuel in it.
Unless you use the drain screw to drain out all the fuel out of the float bowl. (winter storage) thats what the drain is there for. Or long term storage.
So when you take it apart, you will almost always find fuel in the carb.
Now, the pet weiner, when you turn it off, should nto drip or drain, except for the initial fuel still in the fuel line to the carb, that will drip out, after you turn the pet weiner off.
But if it continues to drip. then likely, the pet weiner, is old, and needs rebuilt or replaced.
I mostly plug the end of the fuel line with something, depending on the size of the fuel line. end of a marker pen, ect. inserting it into the fuel line end, when you remove it to clean the carb.
Over the years, I have ran across tons of faulty or old pet cocks, that do not turn off right.
I worry more about if they are clogged or wont even turn at all.
Not that, this is your issue. But the only major issue with a pet weiner not turning off. is that you loose gas and I have seen, a issue with some carbs, where they need work too.
The fuel can flow into the cylinder over a period of a few weeks. way more than what you want !
But don't worry about those examples I mentioned. Normal with age.
Sporty