Green card holders are taxed like US citizens and are thus subject to US income tax on their worldwide income regardless of residency and must also stay FBAR-compliant.
Continuing to hold the card is a status quo maintenance for US tax law purposes.
Don’t be like others who made the mistake of thinking that simply because their green cards have “expired” they are no longer US tax subjects. That doesn’t happen unless it is rescinded or administratively or judicially determined to have been abandoned (think: US Immigration authorities or a US consular officer or an individual’s application for abandonment USING INS Form I–407 ‘Abandonment of Lawful Permanent Resident Status’).
If one leaves the USA with an expired green card but such card remains valid for tax purposes, all the terrible consequences of FBAR non-compliance apply (a nightmare).