What issues would cause all 4 oxygen sensors to need to be replaced

What is your question?

I'm looking to purchase a 2004 Jaguar XJ8. The owners says that it starts and runs find when cold but skips and stalls when it warms up. He says a mechanic came out and told him that the oxygen sensors upstream and downstream need to be replaced. Would bad oxygen sensors cause this type problems? Could it be bad catalytic converters? Thanks

What makes this problem better or worse?

Worse when the car is warm.