"Dripping" is about being caught in a painful relationship and being unable to let go of it, even after it has ended. The speaker remembers sensing from the start that this person would pull them in and tear them apart. The imagery is violent and helpless: being ripped up like paper, screaming, clinging to hope at the edge of a cliff above a "sea of misfortune."
The puppet image is the heart of the poem. The speaker says they were still on the other person's string, ready to be yanked back whenever that person got bored. What stands out is the speaker's choice to keep the string forever and protect it, which suggests loyalty that has turned into self-surrender.
The last two lines add a twist. The speaker admits they aren't in love with the real person, only with the version their mind has built. The mood is dark, bitter, and resigned, with a sad, uneasy honesty at the end.