No. Once Light dies in the Death Note manga, that marks the end of the core story. There may be spin-offs or related works, but the main narrative doesn't carry on from that point.
It focuses on the story of L's early days and how he solves cases. In this novel, we see L's unique detective methods and his battle of wits against various criminals.
One possible fanfiction could be where Light is in the hospital due to an unexpected illness. Maybe he uses this time to plot his next moves in the Death Note world without arousing too much suspicion. He could be pretending to be weaker than he actually is while observing the people around him, looking for potential Kira supporters or enemies among the hospital staff and patients.
A 'death note light x oc fanfiction' often involves creating an original character (OC) and pairing them with Light from 'Death Note'. It can explore unique relationships and scenarios that didn't exist in the original story. For example, the OC might be someone who discovers Light's secret early on and has to decide whether to support him or expose him.
One of the main themes is the battle between good and evil. Light, with the Death Note, represents a form of extreme justice that blurs the line between right and wrong. Another theme is the power of intelligence. Light and L constantly outwit each other using their brilliant minds. Also, it touches on the concept of morality. The use of the Death Note to kill people, even criminals, raises questions about who has the right to judge and take lives.