I've started watching Death Note and I'm a bit confused on an aspect of Shinigami.
In episode 12:
Gelus dies because he killed the would-be murderer of Misa Amane. By doing this he extended the life of Misa for which he disappeared into glitter as they aren't allow to extend lives.
If a Shinigami killed a person at random who was planning to murder a person the next day, he would be extending the life of the victim the murderer was planning to kill. Would the Shinigami die in this scenario?