[jseutter]

I guess it depends on what you call a safe landing. For large airplanes the maximum takeoff weight is typically greater than the maximum landing weight. If an airplane lands overweight it can no longer fly until it has been inspected and repaired. Most emergencies will involve flying around for long enough to get the aircraft within the acceptable weight limit. Some older aircraft have the ability to dump fuel, although I don't know of any new ones that have this capability.

Needing to land before getting under weight usually means a crash landing. In modern times, very few things like fire or an engine self-destructing will require immediately getting out of the air. It is usually better to fly in a straight line, figure out what is going on, figure out where to land, then land. This lets you get underweight, lets you communicate with air traffic control, lets emergency services prepare, etc.