1.) Training on copyright that is publicly available. You write a poem and publish it online for the world to read. That is your IP, no one else can take it an sell it, but they are free to read and be inspired by it. The legalitly of training on this is in the courts, but so far seems to be going in favor of LLMs.
2.) Training on copyright that is not publicly available. These are pretty much pirated works or works obtained by backdoor to avoid paying for them. Your poem is behind a paywall and you never got paid, yet the poem is known by the LLM. This is just straight illegal, as you legally must pay to view the work. However there might be conditions here too like paying for access to an archive and then training on everything in it.