What characteristic of male and female stable flies helps them to feed?

Male and female stable flies possess piercing mouthparts, which are essential for their feeding behavior. These mouthparts are specifically adapted to penetrate the skin of their hosts, allowing them to draw blood, which is their primary food source. This adaptation not only facilitates their feeding process but also influences their behavior, making them adept at locating hosts for feeding.

Other characteristics mentioned, such as flat bodies and wing color, do not directly contribute to the feeding mechanism of stable flies. Flat bodies may assist in their movement and ability to hold onto surfaces, while wing color might be relevant for identification or camouflage but is not functional in the context of feeding. Similarly, a lack of mouthparts would hinder the flies' ability to consume blood, making feeding impossible. Thus, the presence of piercing mouthparts is a critical characteristic that directly supports the feeding habits of stable flies.