The idiom does not seem to be used properly in the second and third examples you give. I have no idea what the intended meaning is for the fourth.
So, let's look at the first. There are areas where people are covered by mental health procedures. And there are areas where people are covered by criminal procedures. But the areas do not align perfectly. There are places in between where this person ended up. Too crazy for jail, not crazy enough for a mental hospital. There was a "crack" between the two worlds and he "slipped" through it.
The final (inasmuch as anyone can tell what Donald Trump is talking about) seems to be about mental health screening and American gun policy. No system of attempting to identify "crazy" people and therefore denying them access to firearms is going to be perfect. For that matter, no system of prohibiting purchase and possession of firearms is going to keep them from the hands of criminals and/or insane people. Any system will have cracks and people will slip through them.
Student or Learner