According to the official description, when a plant dies in Ninjago, a fossilized version of itself appears in the Underworld. These petrified plants are essentially stone; inedible and high in minerals. Like most of the "life" in the Underworld, the plants are completely harmless to passerby.
Everything decays, and when it does, you'll find it in the underworld. Though the fossilized vegetation is not edible, it is a great source of minerals, and a strong proof of life. No reason to worry, the Petrified Plants aren't scared and neither should you be.