They get loose, the plastic tensioner wears, the chain 'stretches' (some say it doesn't actually stretch rather the links wear and it causes the slop), eventually jumps out of timing.
Thats worst case scenario. If you google the issue, it seems to have affected the 06-08 models most, on the golf etc. They changed the oil filter design 3 times, and I believe added an oil feed for the chain directly.
Regular oil changes are important for this engine, for the turbo and chain.
Mine is a 2011 on 76k with no issues, been dealer serviced till I bought it 2.5 years ago, and has had about 4 oil changes in my ownership.