This is the "forbidden experiment"-- linguist wish they new more about this because it has implications for other questions. But doing this to children is barbaric child abuse. So we wait for natural experiments to arise. The best documented ones are the ones Beofett covered, so I won't repeat that part.
The cases of feral children and children locked up and kept from human interaction have the problem that the children are treated horribly and not socialized. So what destroyed their ability to speak? The lack of linguistic input or the fact that they were in situation with no social interaction of any sort?
Well, this experiment is actually on going at the moment every time the parents of deaf children decide not to teach their children sign language. There was one case where parents of a deaf child decided not to sign with their child assuming the kid would pick up English from lip reading-- the child otherwise had loving parents, a comfortable home, toys, etc, just no signing and he couldn't hear anything. And lip reading English is a superpower that doesn't really exist-- so he didn't spontaneously learn lipreading. The kid instead spontaneously created his own signing system that he used with himself. This has happened several times, enough that a researcher was able to examine the various systems in the home sign systems that children created and found novel grammar-- indications that this was a language and not just a few isolated signs, gestures or other things that don't rise to the level of language.
When discussing home sign systems though, at the moment, the topic immediately changes to the incredibly low status of home sign in the US at the moment-- and for good reason, home sign is a shadow of the complexity of ASL and doesn't give you entry to the general Deaf community.
On the topic of the critical period-- it also affects 2nd language acquisition. If you learn a language too long after the critical period, you can't gain near-native fluency. For 2nd language learning, the ability to learn starts dramatically declining at around 11-14 and declines until about 20 where the difficulty of learning a 2nd language stays the same for the rest of the life.
Ref Talking Hands, Margalit Fox