Non-interference engine, like your Corolla: timing belt breaks, engine stops running instantly, replace timing belt, drive on.
Interference engine, like my Neon: timing belt breaks, engine stops running instantly, drain coolant, remove head, replace valves(at least a couple, maybe all
), inspect pistons, replace damaged piston(s) if needed(rare in Neons, but it has happened), buy new head gasket set, replace head, refill with coolant, to be safe change oil & filter, *then* replace timing belt, drive on.
I'll let you decide which is better in the real world.