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First lets clear your question, maybe you meant to say is "How does erosion affect plants?" 
There are three ways in how erosion affects plant.
1.When erosion is happened in one place the roots of the plants will be affected first.
2.Plants will die after  due to erosion.
3. Sometimes erosions contains acidity so when it reaches the other plants, the plant will slowly dry.

(this is what happens to my bestfriends plants when erosion happened to their old house near the sea)