Yes, this really happens. Here is an article by John Lott which lists ten incidents of ordinary citizens stopping mass shootings:
"Permit holders haven't just stopped public shootings. They have stopped everything from public knife attacks to vehicle attacks.
I haven't found a single case where gun control advocates' fears were borne out by the facts. In not one of these cases did a permit holder accidentally shoot a bystander, or a police officer accidentally harm a permit holder."