During her race, Stogner has been accused of holding beliefs antithetical to her party's while taking aim at the oil and gas establishment.
The two challengers, one Republican and one Democrat, hope to unseat incumbent Wayne Christian who is seeking his second term.
The withdrawal brings an end to the years-long effort to construct an oil and gas disposal site in East Texas.
Stogner narrowly edged out Tom Slocum for the second runoff position by less than a percent.
The accident occurred with less than a month remaining in the GOP primary race.
Icy roads are the main problem across the state so far during this winter weather event.
With precipitation incoming, state officials recommended Texans stay off the roads during the next few days as much as possible.
The Texas Railroad Commission regulates the state's oil and gas industry, and Democrats see it as an opportunity to shape energy policy.
The new project will be chiefly aimed at collecting public input from minority and low-income residents around the areas the TCEQ oversees.
A proposed law, intended to discourage flaring, would establish a 25 percent tax on gas flared by oil and gas companies.
With a cash infusion provided by the former New York City mayor, the Railroad Commission race becomes even more contentious despite being overshadowed by other races on the ballot.
Texas oil and gas has taken a hit during the pandemic, but the industry has stabilized some since the initial downturn.
