Is there any short word(s) for "remaining time before death"?
something like "remaining lifespan" or something shorter than "lifetime left"
or something like "lifespan minus age" or "deadline minus current time"
"to live" is a common short form for a specific amount of time as in: "I have four months to live." It's used in technical non-medical senses too. For example DNS, the system by which the URL's you type into your browser are converted to the actual numerical addresses which are required to get your browser to it's proper destination. Each DNS record contains a TTL value - which stands for Time To Live.
For a non-specific amount of time, people often use "time left". As in: "She only has so much time left"
If you're talking about older age, then that is sometimes referred to (poetically) as one's "waning years" or the "winter" of one's life. Twilight imagery is commonly used.
"Remaining life expectancy" would be a more forensic usage -- medical, actuarial, insurance situations.
Other options: Senior years, retirement, end of life, golden years
The best I’ve come up with is “past the veil”. As in “They are already past the veil.” This in reference to the phrase “Death’s black viel” from england. “Whose top-branch overpeer'd Jove's spreading tree. And kept low shrubs from winter's powerful wind. These eyes, that now are dimm'd with death's black veil,” (King Henry the VI, Act 5 Scene 2).
The only serious one I can recall is “three months until their terminal date.”
A few more overly dramatic/poetic turns of phrase include “In deaths shadow”, “kiss of death”, “on deaths door”, “at hell’s gate”(more often a military pre-battle usage) , “valley of the shadow of death”.