Can I fix my bike without replacing the engine?

That piece of dipstick might be caught in the gears between the crankshaft and the clutch basket. Try this: remove the spark plugs, put the bike in gear, release the clutch, and move the bike backwards and forwards. If it suddenly becomes easier to move, hopefully that was the dipstick piece getting dislodged.

After a while, drain the oil and see if the piece comes out. If that happens, compare the piece with your dipstick to see if you got everything out. If not, the next step might be to either cut the oil filter open to see if the missing pieces ended up there, or remove the side cover and look around.

Hope this works out for you, and don’t forget to reinstall the spark plugs and refill the oil. Oh, and needless to say, get a new dipstick before firing it up again.