> *...that person will die in the manner* [*prescribed*].

Non-finite clauses functioning as modifiers in noun phrase structure are quite common. Here, the past-participial clause "prescribed" modifies the noun "manner".

Such clauses are semantically similar to relative clauses: compare *that person will* *die in the manner that is prescribed*.

Past-participial modifiers are bare passives, as evident from the admissibility of a _by_ phrase.

In your example, the modifier "prescribed" could precede the noun with no change in meaning, but it would of course cease to have a passive interpretation.