Contrary to popular belief the seal where the rod comes into the pull start housing is not as tight as a ducks tail.
It wears and allows oil and fuel to venture into the pullstart housing.
When this occurs the one way bearing starts to slip and thus we produce all of the problems that are associated with the Pull start mechanism.
One way to combat this problem is to drill a small hole in the pullstart case (bottom) and one in the top. Use WD40 with the red straw on it to blow out the oil and such that collect and cause problems.
The lower hole provides a drain and allows the oil and debris to escape.

If you are not seeing problems with your pull start slipping then do not use this work around at this point. Some fuel could have found its way in by another vehicle.

You will eventually however began to see the symptoms of what I describe above.
I have never seen a pullstart that did not become wayward at some point.
Your cord being wet may be an indication of things to come.

Dbow