Crank pulley can develop a wobble from either the keyway on the end of the crank or the machined key in the pulley becoming distorted or the vibration damper failing. The latter is just a matter of replacing the damper, which was my circumstances luckily when I reported about my wobble here a year or so ago.
Here's a good crank end keyway:

And here's a good pulley inside:

I had to replace the vibration damper to get rid of a significant wobble there.
My understanding of the crank end damage is that it occurs because the bolt used originally to fasten the pulley to the crank would loosen or stretch while in use, allowing for pulley movement. The old bolts, reportedly, no longer are available and VW now supplies ones developed for the TDI engines. The newer bolts have a button on the end, visible through the crank holder tool I made for loosening the crank bolt:

Somewhere on this site is a write-up about repairing a bad crank end that had really scary photographs of a damaged crank end. However, the write-up lost its images because the place on the web where the author had the pictures posted shut down. So you no longer can see the scary pictures.