Unknownk123, DO NOT WORRY about the colour of the rope / string on the pull start, it could be purple and it would not matter so long as it does it's job. If it gets black and oily, don't worry about it. only worry about replacing it if and ONLY if the cord or return spring snap. Either way, it's easy to restring a pull start, as is repairing the spring, but that's best covered when it happens.
The "One Way Bolt" mentioned by "hpirushrvo" is actually correctly termed the "One Way Bearing". It is most commonly a hex shaped unit that slides onto the starter shaft protruding from the rear of the engine case that also engages into the rope wheel inside the pull start unit. It is not a bolt, it is not a nut (even though it may look like a nut !!), it is a roller clutch (One way bearing).
From what you describe, the OWB has become oily and is slipping on the starter shaft. That DOES NOT mean you have to buy a new one, it just means it needs cleaning.
All you need do is remove the pull start unit, then the OWB (One way Bearing) noting which way the OWB comes off as this is the way that it has to be refitted, especially since it will only rotate in one direction.
To clean the OWB, either wash it through with some WD40, Denatured alchohol or fuel then roll the clutch around a soft lint free cloth that has been pushed through to simulate the starter shaft, then wipe the outside and put to one side.Next, clean the starter shaft as this too can become oily enough to cause the OWB to slip.
All you need to do once that is done, is replace the OWB & pull start unit and test for function.
Hope that helps you........