The assassin snails do not eat their own eggs or other assassin snails under any normal circumstances. While I have not seen it, I guess it could be possible under extreme hunger standards of a neglected tank They have a marker that causes them not to predate each other. If a assassin snail dies it will be eaten by live ones for sure. No need to pull out the eggs at all.
First off I must say I know their shells are in a pretty rough condition, unfortunately they came from a tank with low pH and they suffered from erosion. Luckily in their new tank the water levels are adjusted and they're doing very well.
The two went back and forth for a while each sending out their mouth tubes and nipping at each other as well as swinging their shells to hit each other. After a while the new comer decided it wasn't worth the effort and took off. I've seen my snails mate a ton since but never any fighting. Kinda odd.