Does Mycelium Die After Fruiting?

Neither. The "mushroom" is simply the fruiting body

of a mycelium structure that continues to live long after the mushroom is picked. The mushroom is just like an apple. The mycelium is the tree.

Does mycelium die?

The mycelium is there throughout the year, in the soil or in the log, and is not a static object. It grows and may die.

How do you keep mycelium alive?

For a while, providing enough nutrition to the mycelium is like feeding a pet to keep it alive. Your role is to give them enough food, fattening them up by feeding them on organic matter. But then, you actually have to starve them because mushrooms only fruit when they run out of a food source.