It depends on the aircraft. The FAA requires (and therefore every airline that wants to fly to the US has) fuel dumping if the aircraft cannot perform a go-around (aborted landing) after an engine failure. A modern twin-engine aircraft can do this so they omit the complexity and weight of the fuel dumping system.

If the worst happens an overweight landing is an option, it's just not desirable. The landing gear should be able to handle it without collapsing but may take significant damage.