Lambda sensor is in exhaust. It measures the air/fuel ratio what has burned in cylinder. All EFI cars don't have this at all.
MAF sensor (mass air flow) is usually after air cleaner and measures the mass of the air getting in.
MAP sensor (mass air pressure) is in intake manifold, after throttle body and measures the air pressure. Cars with MAP usually don't have MAF I believe.
Getting rich fuel ratio doesn't usually brake engine, lean does. Rich may broke the catalysator tho.
Modern engines are very sensible so I can imagine them suffering from rich ratio, but I can't be sure.
If you change the circulating BOV to atmospheric one in some cars it may have a tiny effect on the air fuel ratio, I'm actually not perfectly sure why, because MAP and MAF are used to measure how much you need fuel.
I have never heard anyone braking catalysator with atmospheric BOV, but it is told as a common fact in some modern cars so I can't deny.
Good thing I'm never going to own a catalysator (I hope).
BTW injection cars stop supplying fuel when the throttle is closed and the car is in engine brake.