Property gifted to you is property of the bankruptcy estate. An engagement ring, jewelry, family heirlooms, are all items that are included in a bankruptcy estate. The mere fact that you received something by gift does not alter your ownership interest. You simply own it whether you paid for it or not. Can you give it back? Yes, but that transfer can be avoided in bankruptcy, which means in bankruptcy the person appointed to oversee your case can recover the jewelry that you gave back. The bankruptcy estate includes all property that a person may have sentimental or emotional attachment and that attachment can be so strong that a person opts not to file for bankruptcy.
If you chooses to look into bankruptcy, the bankruptcy estate includes most property and is defined in 11 USC 541 (a) The commencement of a case under section 301, 302, or 303 of this title creates an estate. Such estate is comprised of all the following property, wherever located and by whomever held: (1) Except as provided in subsections (b) and (c)(2) of this section, all legal or equitable interests of the debtor in property as of the commencement of the case. Property of the Estate