they should sell a replacement recoil assembly if that's what you are referencing.
you have some pics you can put up or a model number we can help research?

This might be what you are looking for but you would have to check using the model no/engine type.

https://www.jackssmallengines.com/Products/JOHN-DEERE/Starter-Part/Starter-Clutches

See if there are any brand name or numbers/marking on the engine. Might not be a John Deere engine. Then google should turn up a manual and parts list. Then a search should turn up sources.

If it isn't a John Deere engine, they might not be a parts source.

LTG : )

Sometimes you can spray WD-40 up into the mechanism and lightly Tap dead center on the top while pulling the rope and allowing it to recoil.

The small steel balls that are slung out with centrifugal force and engage with the motor get gummed up. Never seen one that needed replacing.

If phil-lee's idea doesn't work; Send [email protected] a quick email regarding this. He might be able to help.

Search “engine recoil pull starter” on Amazon and you might find what you’re looking for for under $20.