Necessary Employees and Persons Authorized
Does it mean "(necessary employees) and (persons authorized)" or "necessary (employees and persons) who are authorized"?
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It is ambiguous, but given the specific context, it would be more common for it to be treated as two things:
Part of the problem is the order of the words in the second phrase. More commonly, authorized would come before Persons:
In which case, the full version of the sentence would be more understandable:
Necessary Employees and Authorized Persons
In the original version of the sentence, by having put Authorized at the end of the sentence you are creating the possibility that it applies to either just Persons (which is typical) or to Employees and Persons. But note that if Authorized applies to both, then it would also be possible for Necessary to apply to both.
If you really do want to have both modifiers apply to both nouns, then you would likely write it differently:
Necessary and Authorized Employees and Persons
This makes it clearer that the combination of two nouns is being modified by a combination of the two adjectives.