As a person who had parts of his work plagerized....i would say it depends. Lifting the entire poem is illegal without permission from the owner, if said owner has a copyright, and punishable by law.
Lifting a sentence, or phrase is harder to prove. If the line is stolen verbatim, it would'nt be worth hiring a lawyer to pursue it, and a judge may not even take the case.
The fact of the matter is, we all in some way are guilty of a lesser form of plagerism. There are our favorite writers, who we may be heavily influenced by, so we may lift the tone or spirit of the piece, but not the words. We are all influenced by our environment, which includes other writers.
Online, it may be easier to prove, being that you can bring up the page...but it takes time, and you have to prove that they impeded you making a profit, or they gained a substantial profit from said work.
I know this, because I had a case.