I don't think this is the right use of tồn tại. This word is supposed to be applied to inanimate objects, like a building that still exists after an earthquake. To apply it to a person is considered rude. For instance, applying tồn tại to describe an elderly man who is stubbornly hanging onto life even though he is so old.
Interesting. A native speaker said it is okay to use when referring to a person but it has other meanings. I didn't understand what she meant. Can others weigh in on the meaning and use?