reason for it being unplugged... my guess it threw a fuse (the one for the fuel pump) which will logically make the engine stop....
with lambda disconnected it would use a default value.... which is chosen to be slightly rich mixture (less damaging than too lean).... probably checked how much a new one of them was and decided to f**k it (or the old one is stuck he couldnt be bothered to get it out.... hate when people do this....
bet it's not the only issue with it...
I would try to replace lambda sensor, go for a decent quality one... then hook it up to vcds and check it works again (check the vagcom/vcds user list in the garage section). then test in garage if cat was damaged.