What you're talking about isn't called a "dependent clause"; it is called an "absolute phrase." An absolute phrase joins a participle with a noun in order to modify an object outside the phrase.
It's appropriate to use an absolute phrase when you see fit, usually at the beginning or tail end of a sentence or clause. By the way, such a phrase can also be called a "participle" or a "non-finite phrase." You may hear the term "dangling participle" when such a phrase introduces a sentence improperly.
Running late for work, the car wouldn't start for John.
The text in bold is an absolute phrase that is often referred to as a "dangling participle" as it's clearly not about subject. It is not the "car" that is running late for work but "John."
An absolute phrase that introduces or trails a main clause is typically understood to relate to the subject, not the object. As such, in your example sentence, it is "Congress" (or "Congress passing") that is "increasing the price of imported goods." That is to say that "increasing the price of imported goods" modifies "Congress" and how it "passed." It can be a hazy line with absolute phrases as to whether they adjectivally modify the subject or adverbially modify the verb, so many simply say that an absolute phrase modifies the subject/verb.