A basilisk kills on contact with vision, but when Voldemort dies, he enters an apparition-like state (bodyless, but not completely detached from the world).
Would staring at a basilisk in this state kill someone who had been reduced to this state by a Horcrux?
Whenever Voldy dies, his Hurcruxes keep him alive in a bodiless form.
I was ripped from my body, I was less than spirit, less than the meanest ghost . . . but still, I was alive. What I was, even I do not know . . . I, who have gone further than anybody along the path that leads to immortality.
(Harry Potter and the Goblet of Fire - Chapter 33)
In this state a Baslisk would appear to have no effect because:
Voldy later used some weird, presumably dark, magic do give himself the famous form of a "hairless and scaly-looking", "dark, raw, reddish black" "crouched human child" with "thin and feeble" "arms and legs" and a "flat and snakelike" face, that we know and love throughout most of Goblet of Fire.
“Wormtail’s body, of course, was ill adapted for possession, as all assumed him dead, and would attract far too much attention if noticed. However, he was the able-bodied servant I needed, and, poor wizard though he is, Wormtail was able to follow the instructions I gave him, which would return me to a rudimentary, weak body of my own, a body I would be able to inhabit while awaiting the essential ingredients for true rebirth . . . a spell or two of my own invention . . . a little help from my dear Nagini,” Voldemort’s red eyes fell upon the continually circling snake, “a potion concocted from unicorn blood, and the snake venom Nagini provided . . . I was soon returned to an almost human form, and strong enough to travel.
(Harry Potter and the Goblet of Fire - Chapter 33)
In this state, which possess a body and eyes, we can assume that looking at a Basilisk would either:
The answer would depend on whether this new body is considered alive or not. I would go with the former, but considering the never seen before magic used to create this "body", I really have no idea.
The Dark Lord, when he’s ripped from his body, existed in a spirit form. He can’t be truly killed while his Horcruxes ensure he stays earthbound, so looking at a basilisk wouldn’t kill him as he couldn’t die. Having Horcruxes meant his soul couldn’t ‘move on’ while they were intact - he couldn’t die.
“Well, you split your soul, you see,’ said Slughorn, ‘and hide part of it in an object outside the body. Then, even if one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
Since the Dark Lord after being ripped from his body is similar to a ghost (though not quite one), it seems most likely that he’d be Petrified similarly to how a ghost would be.
“It was Nearly Headless Nick, no longer pearly-white and transparent, but black and smoky, floating immobile and horizontal, six inches off the floor. His head was half off and his face wore an expression of shock identical to Justin’s.”
- Harry Potter and the Chamber of Secrets, Chapter 11 (The Duelling Club)
Though it’s in no way certain that the Dark Lord would be Petrified if he looked at a basilisk while in spirit form, it seems to be the most likely result from what’s known about what happens when other types of spirits look at a basilisk. He seems clearly able to see while in spirit form, since right after he’s ripped from his body, he sees the Potter house had turned to rubble and Harry was trapped. He was only just ripped from his body, so wouldn’t have had a chance to possess anything else yet.
‘Avada Kedavra!’
And then he broke: he was nothing, nothing but pain and terror, and he must hide himself, not here in the rubble of the ruined house, where the child was trapped and screaming, but far away … far away …”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
This shows that the Dark Lord was able to see in spirit form, so he would be capable of looking at a basilisk. Since he can’t die, and other spirits get Petrified, it seems most likely he’d get Petrified.
