Catch it, of course!
Failing to catch it will result in splatter
That guy loses, and you should report his error to his management.
Hopefully that guy will learn to be more careful about how he catches his next egg.
In the interim, he's out, and you've lost a program.
Catch it, of course!
Failing to catch it results in every other egg thrown at X falling and you get upset. It's your job to report that X was bad at catching eggs to the people responsible for X.
All eggs are created equal, anyone can send the exact same series of eggs to X. It just happens that today it was Firefox which tossed the egg.
But tomorrow it might be someone else. And they might be malicious, or just careless.
The neat thing about these eggs is that when they're reproducible, people on all sides are happy, because reproducible eggs are catchable eggs. They can be made into poached eggs since you can toss them again and again until you catch them.
This is much better than simple scrambled eggs with no hints and lots of suspects. This can happen if the kernel reboots or X doesn't leave a log and you weren't there to watch (think about a Tsunami or an Earthquake, the world shifts, and there's wreckage when you return but no sign of the culprit).
Help make the world a better place, report that dropped egg and get it caught the next time.
Well, normally in dodgeball, people intentionally would bean X. Here X is more like the reluctant father who was coerced by his family into playing.