I have been at Mass three times when this has happened. Once the priest summoned the usher and whispered something to him, but Sunday Mass continued without missing a beat. At the end of Mass, I think the priest did ask us to keep the person in our prayers.
Another time, a lady fainted during daily Mass. It was right after the homily as the priest was offering a prayer of petition. He stopped in mid-sentence, went to the lady who was in the front row, instructed someone to call 911, and anointed her. We waited until the fire truck and ambulance arrived and did their thing. After they left, Mass continued. Most people stayed, and Father thanked us for that.
The third time was a Sunday Mass, and I didn’t realize that anything was amiss until we left Mass and saw a fire truck in front. I think that time it was someone who wandered in from the street, and the action may have transpired in the vestibule or even outside.
When I was in second grade, I was in church when a tornado hit. The roof was torn off, and i’m pretty sure Mass stopped at that point. I remember seeing the priest walking around inside the church later with an umbrella.