Not necessarily. The amplifiers sometimes are though.

In a normal 2 or 3 way speaker cabinet, you'll have an analog crossover which consists of something like a capacitor in series with the tweeter (high pass filter), and an inductor in series with the woofer (low pass filter).

In that case, the tweeter is protected from DC, but the woofer isn't.

Yes, it's unlikely to cause problems in any real-world setup, but it's theoretically possible :P I've edited my original comment to clarify that it won't always be the case.