In addition to implying an on-going activity of a verb, vs a verb whose action is completed, an "-ing" ending can effectively convert the verb to a noun. In the first sentence "adhering" is functioning as a noun (though you'll start a nasty argument from some people if you try to claim it is a noun -- "gerund" is the more proper term). With minor modifications it's possible to make your #2 work, but not as it stands.
Note that in the first sentence the prepositional phrase "to established security procedures" can be removed without changing the fundamental syntax or semantics of the sentence. The phrase is being used as a modifier (adjective) for the gerund "adhering".
The second sentence can be reworded as "Properly adhered to, established security procedures represent that clients' confidential information is being protected." In this case "to" is being used as, I believe, an "infinitive marker". The sentence is still a little awkward, as "that" is being used as a "determiner" rather than a regular pronoun, and the structure of that sentence does not make this clear until the reader gets a parsing error (due to his incorrect initial assumption) a few words further on.
(And as FF suggests above, you could alternatively change "adhered to" to "adhered-to" in the second sentence, making it a modifier of "established security procedures".)