So according to this website https://eigobu.jp/magazine/hodasareru some 類語 of 「絆される」 are "押し切られる; 呑まれる; 丸め込まれる; 力負けする; 手折られる."
Of course, Jisho just tells me that this word means "to be moved by kindness" but these 類語 make me think it can be translated as "to be outmatched [by]" or "to be overwhelmed [by]" or "to be outwitted [by]" in some cases.
I'm translating a song about a guy trying to capture a villain, and in this context, I think the 類語 definitions work better. Also, the villain is the 妄想 in the story; he's the speakers evil alter ego that he doesn't fully realize exists yet. As such, he indirectly refers to the villain as the 妄想; it is personified (I think)。
I really don't think this means "moved by kindness" here as the two continue trying to kill each other in the song. Can I use the word "outmatched" or "outwitted"? (I think I prefer outwitted since it has a connotation of losing to someone in a mental game, which might be similar to 絆される in my opinion.)