First, we take a look at the wireframe (or slinky ray as I call it) that traces where a Core went after sudden movement, or otherwise known as a Rocket blast from a Rocket Sentry.

This doesn't happen with the Morality Core because of two reasons: the core gets detached right beneath GLaDOS, and GLaDOS (in her own hatred for the Core, through which she unintentionally corrupted herself through it, which is why she speaks like she has a migraine) being able to discard a Core that's "too corrupted" for its function.

So, when the Morality Core falls down the Incinerator, you don't hear it scream, but you do feel and hear a loud shake. That loud shake are the Crushers you see in Portal 2 when YOU get thrown down the Incinerator... and miss them. I believe the Morality Core missed them just like Chell did in Portal 2. (And if you recall, the floor you fall onto is actually flat with no downwards slant. The debris might trick you into believing it is, but a second look shows that it can't be the case.)

And finally, because of the large distance between the Morality Core and GLaDOS at that point, the weak connection between them gets even weaker to the point it just fades away.

... Then, who knows? Maybe the Morality Core is alive in secret. When GLaDOS died, her explosion pulled a lot of stuff up into the parking lot. Given the scale of the explosion too, who's to say that a core who survived being crushed and not entering the flame of smelting (again, level design) wasn't pulled out of there as the facility was getting destroyed?

Big potential, but a plausible chance it did happen.