Symbolism, Imagery, Allegory
If the coyotes symbolize the raw, animal mayhem that takes over the play, the houseplants symbolize the normalcy that is destroyed.
While at his mom's house to write, Austin is supposed to water the plants. There are quite a few plants, but it's not like this is a difficult task or anything. Of course, considering what they symbolize, we're sure it's no surprise that things are not going to end well for the houseplants.
These plants, along with Mom's knickknacks and even the neighborhood she lives in, symbolize the normalcy of everyday suburban life. Sure there are still some coyotes out West, but they're not the norm in this new land. The West is just like any other place, filled with nice little houses and nice little houseplants. By the end of the play, this suburban image is shattered by Austin and Lee, and Shepard makes it a point to show us this through the death of the houseplants:
All of their mother's houseplants are dead and drooping (2.8.13-14).