The first problem is any mechanic that "thinks" the 02 sensor is bad is a hack! Any decent mechanic would hook up a scan tool and watch the 02 sensors voltage readings and switching time to make sure what's going on with the 02 sensor before just guessing! If the car just shuts off while driving it may be a crankshaft senor beginning to fail. When it stalls you need to check for spark and injector pulse. You won't have either if the crankshaft sensor is bad.
Sure, it could be the O2 sensor. But it could also be any number of other issues as well.
A bad O2 sensor will usually cause the engine to default to a rich condition ( running rich does less potential harm than running lean ).
A bad O2 sensor would trigger a check engine light.
IF either of the two oxygen sensors were bad the check engine light would be on.
#1. Replace the fuel filter first.
#2. Take the car to a Dodge Dealer and ask them to test the fuel pressure on the fuel rail pressure fitting. This is a very inexpensive test BUT the fuel filter must be clean to get an accurate fuel pressure reading.
#3. When was the last time the motor had an electrical tune-up? If the car had over 100,000 miles on the odometer it's well over-due.
Sure, you can either get too much or too little fuel if the O2 sensor is not working correctly.
Highly unlikely that it will cause a stall while driving, get another mechanic.
My dad has a 2004 dodge stratus (2.7 engine) and it stalls when he's driving. The mechanic told him that there could be something wrong with the 02 sensor. Could that be the problem?