Final answer:
Cabeza de Vaca stayed alive by being perseverant and adaptable.
Step-by-step explanation:
The quality that helped Cabeza de Vaca stay alive was his perseverance and adaptability. As a Spanish explorer stranded in what is now Texas, he was able to survive by learning from and living with the indigenous people. He adapted to their way of life, learning their language, customs, and survival skills.
This quality enabled him to survive various hardships, including hunger, disease, and dangerous encounters. He was able to build relationships with the natives, which eventually led to his rescue and return to Spain.