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Your consciousness stops for you in both scenarios. In the teleporter scenario a clone lives out the rest of your life. To everyone around you its as if nothing has changed but for you, specifically, time stopped progressing at the sending-teleporter.
Just because the second verse literally has its own implied threat does not mean the first verse is unrelated. In songs and paragraphs adjacent sentences are typically related- its how English works- but I can’t speak for all languages.