In The Goldfinch, the characters are chained just like the bird in the painting. Sometimes these chains are physical, and sometimes they are emotional.
Theo is deeply affected by the trauma he experiences as a child during the bombing. Over the years, he experiments with drug abuse. In Las Vegas, Theo and Boris spend their days using drugs. Years later Theo becomes addicted to prescriptions. He becomes chained to drugs.
Theo is also chained by his guilt. As an adult, he feels guilty for taking The Goldfinch painting as a child. He also sells fake antiques and is weighed by the guilt of this. Boris also feels guilty, as he reveals he took the painting back in high school. Their guilt leads them on a risky recovery trip, and eventually they are able to get the painting to a museum. Theo uses the reward money to buy back the fake antiques, therefore freeing himself from the guilt.
While in the hotel after Boris is shot, Theo feels trapped. He drinks and almost commits suicide to free himself from the chained feeling.
Pippa fights against the chain to her traumatic experience and avoids getting tangled in Theo's chain. Although they share an emotional bond, she will not be with him.