I’m guessing here, but the cartel probably put her in the trunk of a car and drove her to Mexico that night.
No need for Mexico. There is nothing much between Tuscon and Nogsles other than cactus and scorpions. She was in a hole in the desert by dawn.
Or put her in a faraday cage.
I’d guess 90% sure she is dead and didn’t survive the initial abduction.
Why would the cartel be looking for this attention? Or have such a bungler on the job?