If it was a tire that got sucked into an engine, must have been from the nose gear. The main gear is behind the engines as can be seen on this photo of a 767-300.
Now that right there would have had me over the edge...What made it even more unnerving was the Baptist women's group singing "Amazing Grace" as we made our descent.
I was on a 727 that lost an engine.
It was back in the late 1960s-early 70s. I was flying from Iowa enroute to Oakland, California with my brother. Before boarding we were watching our plane taxi up to the boarding dock and noticed some flames shooting out of the front of one of engines. Something I'd never seen before. We were hesitant but boarded the plane and a short while later while at cruising altitude we felt the plane suddenly dropping repeatedly. Then the captain announced, "We've lost #2 engine and will be doing an emergency landing at Denver Airport."
On final approach to Denver we were flying extremely low. It seemed we weren't more than about 50 feet at times. I remember passing a cow pasture and clearly seeing cows watching us pass and we weren't much higher than they were! I looked forward and could see the start of the runway and it was actually above us at one point. The pilot had to pull up to gain altitude before touching down on the runway. Sheesh!
Anyway, we landed without incident and all was well. Whew!