When Spartans inspected babies and "bad babies" were thrown off a cliff, what happens if a baby survived from being thrown off a cliff?

It never happened. It's pure fantasy. The only source to suggest such a thing is Plutarch's Life of Lykourgos, and Plutarch is not very reliable at the best of times. More importantly, the Spartans had a long history of falsifying and mythologising their past, so even a careful and sceptical source in Plutarch's time would hardly be able to determine any real information about anything that far in the past. The only contemporary source on the Spartan agōgē is Xenophon's Constitution of the Lakedaimonians: in Xenophon's time it would have been difficult for an Athenian to obtain reliable information that wasn't tainted by propaganda, yet even he mentions no nonsense of this kind. So it's not just a fabrication, it's a late fabrication.

It would in any case be insanity, in a society that was running seriously short of population for its ruling class, to institute a law that killed them off at the slightest excuse. Plutarch also tells us that in classical Sparta babies were bathed in wine, and that there was no such thing as adultery. That doesn't mean any of it is true. He does occasionally get things right about the distant past, but only by accident, and we can only tell that he's right if external evidence corroborates him.

Here's some further reading. Kennell's book shows pretty clearly that the picture of the agōgē that Plutarch gives us was made up in the Hellenistic period, and that Plutarch revived the story a few centuries later.

Hodkinson 1997, "The development of Spartan society and institutions in the Archaic Period", in Mitchell and Rhodes (eds.) The development of the Polis in Archaic Greece 83-102, at 83-7
Kennell 1995, The Gymnasium of Virtue: Education and Culture in Ancient Sparta (Chapel Hill)
Van Wees 1999, "Tyrtaeus' eunomia: nothing to do with the Great Rhetra", in Hodkinson and Powell (eds.) Sparta: New Perspectives 1-41, at 14-22