Yep. Now we are on the slippery slope of Pleistocene Re-wilding via proxy! . There are no effective predators (cougars and coyotes might take calves...which can control or even depress ungulate populations, witness the Muskox on Alaska’s Arctic Slope) of adult Nilgai in Texas, although I am sure cougars take the occasional adult. But I imagine that human hunters and vehicles are the most constant predators. Although the isolated area in which they live and the size of the private parcels (some behind high fences) they inhabit probably reduce the “effectiveness” of road accidents (I know, I know) to control the numbers. By law I believe all non-native wildlife in Texas (outside of specific animals in very specific areas) are considered “livestock” and the property of the land-owner.
As of yet, I don’t believe Black Bears inhabit the South Texas plains...but over the last few decades they have spread across the Rio Grande, further north and west, in the area of Val Verde County and will likely eventually repopulate the Nilgai’s range. Once they learn to hit calves, the Black Bear might be a very effective predator of the Nilgai. Here in Alaska, where they coexist, Moose calves are a primary food source of both Black and Brown Bears in the Spring. Probably won’t be able to control Nilgai numbers completely once Bears reach their habitat. Ultimately environmental factors and urban development will limit the spread of the animal.