Bit late I know we did an A4 BLB engine same problem, fortunately the engine was only ticking over when oil light came on.
Chain wheels worn to excess and chain snapped !

Replaced balance shaft housing complete with genuine Audi parts, £900.00 but comes with gear drive to replace chain and a new sump.
Bit of a problem getting old gear off the crankshaft nose and had to make a tool to keep shafts in correct alignment but otherwise relatively straight forward job.