The Hashiras would likely show concern. Some, like Shinobu, would immediately start looking into possible medical solutions. Giyuu might be more reserved in his worry but would still keep a close eye on Tanjiro. The other demon slayers would also be affected. They look up to Tanjiro, so his sickness would lower the morale of the group. They would try to support each other while waiting for Tanjiro to recover.
There could be a fanfic that focuses on Luigi's training to control his death stare. He might seek out the help of a wise old Toad who has knowledge of ancient powers. This would make for an interesting story as Luigi tries to master this power without causing harm to his friends.
It often shows the fragility of life. For example, in many post - apocalyptic sci - fi stories, characters are constantly facing threats that could end their lives. This makes the reader or viewer acutely aware of mortality.
There might be a fanfic where Luigi's death stare is misinterpreted. His friends initially think he has turned evil because of it, but later they discover it's a new power he has gained to protect them from a hidden threat that can only be detected by this intense stare.
One notable work could be 'The Andromeda Strain'. It involves a deadly extraterrestrial microbe that threatens humanity, with scientists racing against time. The 'stare of death' aspect can be seen in the sense of the impending doom that the microbe represents.
The lack of emotion in the stare can be very creepy. If it's just a cold, dead stare, without any hint of humanity or kindness. It gives the impression that whatever is doing the staring is not alive in the normal sense, or that it has no empathy. This makes the person on the receiving end feel very vulnerable and scared.
Tanjiro might use his sense of smell to detect hidden threats. Since his sense of smell is super - enhanced, he could sniff out any demons or traps in the way of saving Rengoku. For example, if there are demons disguised as allies, Tanjiro would be able to tell by their scent.