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.

It is unidiomatic to remove the subject and verb in the dependent clause (i.e. it is), when it follows the independent clause. Thus, 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.

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.