From doing some research, I think this might be a type of monkey grass (specifically, a variety of Liriope Muscari?). I'd like to look up how to care for it, as I'm not sure if I can trim it back now (it's early October in Tennessee as I write this) or if I should wait until it's dormant in winter. I've been living in my place for less than a year, so I'm trying to figure out what all the various shrubs we have are, so that I can care for them appropriately.
There are a couple of them in a row here, and they have purple flower stalks that appeared in the last month or two:
And here's a close-up of the flower stalks:
Thank you!