The two examples are not a sentence and it is not meaningful to classify "shot to death" as "adjectival phrase". In newspaper headlines, it is common to omit the verb to "be" and an article because it doesn't cause confusion and the headlines need to be as concise as possible. It should be
A UCLA engineering professor was shot to death in apparent murder-suicide
The preposition to is used as
a function word to indicate the result of an action or a process
In both of your examples, "to" indicates the result of an action to "shoot".
As @BrianDonovan commented, "to death" is a prepositional phrase which is functioning as an adverb, and it modifies the action to "shoot". A good example is "He drank himself to death" which could be rephrased to "He drank continuously until it caused his death".
Active voice of the example should be:
A student shot a UCLA engineering professor to death in apparent
murder-suicide.