Ask Mr. Smarty Plants

Yes, sedges would be a good choice since they do well in shade and have few disease or insect problems.  Mr. Smarty Plants recommends several sedges, all of which survive dry conditions but look nicer if watered.  In the order of increasing plant height, Carex planostachys (Cedar sedge) (6 in.), Carex retroflexa var texensis (sometimes called Texas sedge) (6-12 in.), Carex texensis (Texas sedge) (10-12 in.) and Carex blanda (Eastern woodland sedge), also called Creek sedge and Stream Sedge (1-3 ft.) should all grow well in Dallas.  For more information on sedges, see the McNeal Growers web site, where you could purchase Texas sedge and Eastern woodland sedge. It may not be easy to find Cedar Sedge in nurseries although I notice the the Dallas nursery Repotted lists it.  Other local suppliers are listed on the Lady Bird Johnson Wildflower Center web site. Look for the latin name you want, since many different common names are sometimes applied to the same sedge species.

As an alternative, consider a grass, Tridens muticus (Slim tridens) (1-3 ft), which forms a gray-green clump about the size of liriope and grows well in partial shade, or Setaria scheelei (Southwestern bristlegrass), (1-2 ft),which has wider, greener leaves and attractive seed heads that birds like.  You might have to look in nature for the bristlegrass seeds or purchase seeds of a related species, Setaria macrostachya, Plains bristlegrass.