Cut the Cord
In the prologue, a nine-year-old Margo Roth Spiegelman wonders why the man she found in the park killed himself. "Maybe all the strings inside him broke" (Prologue.32), she says, because nine-year-olds love speaking in metaphor.
She brings up strings again later, saying that "Every paper girl needs at least one string, right?" (1.6.35). When she does, she's talking about her friends—people she doesn't really like—and how they were pretty much the only thing they had left.
Quentin wonders about all the string talk, and thinks it might be Margo's suicidal tendencies talking. If all her strings break, is she going to kill herself? Quentin doesn't want that, so he tries to find her and be the string that she can follow back home. Strings, then, stand for connections, whether they're wanted or not.
Follow the Wind
All the string imagery ties into Detective Warren's assessment of Margo Roth Spiegelman as a balloon. (No, Margo Roth Spiegelman, this isn't a comment on your weight—put your spray paint away.) He calls her a "free spirit" (2.3.41), noting that "that string gets cut all the time" (2.3.41) in reference to her repeated disappearances. Margo, then, cuts her own string. And without strings, balloons just float away, which is exactly what Margo does. And she doesn't want to come back. You go be you, Margo.