It is not impossible that we will prove LLMs are not possible to fully safeguard.

If someone told you "i can guarantee Fred Smith here will never, ever say anything inappropriate. He's not capable of it." (Fred being a regular old human.) You'd say "Well, no, you can't guarantee that. You may have given Fred all the best training in the world. You may have selected Fred from 10,000 other candidates as the least likely to ever say anything inappropriate. Fred may have strict instructions not to. But he still could."

It may be the same with LLMs.