There is no default backup setting if the oxygen sensor is unplugged, so not sure that is a good idea. If you do unplug it, then only leave it unplugged for short periods, otherwise the catalyer could be damaged.
My money is on the fuel pump itself being faulty.
eh? YOU are the one that said it had no default map?
I said it doesn't matter what 2.0 16v I was talking about because I was trying to make you see that no lambda isn't the end of the world for a cat, its fine without one. As you say it catches any other problems with the injection system, but it will still run fine without and wont damage the cat unless something else is wrong. I know the K & KE Jet are completly different to the VR6 system, please don't try to make me sound like an idiot 
The default fuel map will NOT damage the lambda on its own. I have no idea what point you were trying to make really! 
Right lets start from the beginning again.
If the lambda has no signal then you said that the ECU runs off a default map.
For the ECU to run off a default map, you need either a back up sensor/s for the ecu to make the calculation, or a default setting for the sensor.
In this case the lambda has no back up sensor/s, neither does it have a default reading.
So as i said in the first place, which is exactly what that guide says, no signal means no regulation, basically meaning the ECU will ignore the sensor.
I'm not saying that if you unplug the lambda that you will deffo ruin the catalyser. It just something i wouldn't risk myself in the long term because that sensor is basically there to protect it.
I'm not trying to make you out as an idiot, just pointing out what i think mate, don't take it so personallyÂÂÂ

If you read through the whole lot again i think we are basically saying the same thing anywayÂÂÂ

We both agree that the engine can run without the lambda sensor, we both agree that the map will be slightly different, as there is no lambda input.
What we are effectively disagreeing about is whether the lambda has a default setting, or whether it is just completely ignored.
The map could be the same or just a modified one with the lambda sensor ignored, i think it is probably the same standard map with the lambda ignored, what i don't agree with you about is that the lambda has a default setting, as it doesn't.