Learn English – “The influence of … on/upon …”

In the sentence,

Unless disciplined, a dog becomes a household pest

unless is a conjunction*. This sentence is really a reduction of

Unless it is disciplined, a dog becomes a household pest.

The conjunctional function becomes clearer upon a rearrangement of the clauses:

A dog becomes a household pest, unless [it is] disciplined.

The most likely constructions a native speaker would use are the following:

• A dog becomes a household pest, unless it is disciplined.
• Unless it is disciplined, a dog becomes a household pest.
• Unless a dog is disciplined, it becomes a household pest.
• Unless disciplined, a dog becomes a household pest.

*I see how unless could be said to be used as a preposition:

A dog becomes a household pest unless disciplined.

(No comma before unless and disciplined becomes an adjective.) I doubt this is formal usage, though. Before the independent clause, however, I would always take unless as a conjunction.

According to William Strunk's Elements of Style (Chapter 3, suggestion 15), "an article or a preposition applying to all the members of a series must either be used only before the first term or else be repeated before each term."

In other words, either approach is acceptable as long as you remain consistent.

I'd say that in general the prepositions should be omitted unless you want to emphasize that the items in the list are separate.