1999 Ford Mustang Can damged oxygen sensor cause other prob

I recently ran over a chunk of concrete in the road that was too large to straddle. I immediately detected an exhaust leak. The check engine light came on shortly after that. My car began to stutter a little when gassing it. I had the code checked out and it said I had a malfunctioning oxygen sensor. When I repleced the sensor, it was visibly damaged. I had taken my negative battery cable off as I replaced the sensor. My car still stutters when I gas it and no check engine light came back. Is there anything that a bad oxygen sensor could have caused? I have always taken great care of the car, but I am not sure what mods may have been done to it before I purchased it!