Does a risk of death exist in the awakening process?

I have a vague recollection of a Dhamma teacher saying that, in the process of awakening, the practitioner eventually reaches a stage of development where they either awaken fully or they die. I'm not sure if my memory of this is correct or not. I have a vague recollection of the Dhamma teacher treating this as a myth which is not to be taken seriously. For this reason, I may have discarded it. However, I am intensely curious. Is anything like this mentioned anywhere in the suttas?