First, it is more correct/natural to say people were chosen from a group of candidates, rather than among a group of candidates, so I would recommend the use of "chosen from" rather than "chosen among" here.
Regarding your main question, using a preposition followed by an interrogative word, such as "from who" (or other combinations, like "of which", etc) indicates that you are creating a subordinate clause to add information to a preceding noun (and requires the use of an objective pronoun ("whom")):
the students from whom the applications were received.
(here "from whom the applications were received" is modifying "students")
However, in your sentence, there is no preceding noun to modify, so this is not right.
In order to make this work, you need some noun before the subordinate clause for it to modify, and that is the purpose that "those" serves. That noun can then be modified by a dependent clause ("who were unable ...") to make it more specific:
chosen from those who were unable to enter any of the schools they applied to
Here, "who were unable to enter any of the schools they applied to" is modifying "those", which creates a group of people to be the object of "chosen from", which is what you intended.
So no, you cannot leave out "those" in situations like this, because "who" starts a dependent clause which needs to modify some noun that comes before it.