I absolutely agree with Gilbert and JW. During my asylum case I was represented by a prominent New York City attorney, Alan Lee. And he told me in no uncertain terms that DO NOT RENEW your passport.
Mr. Lee provides community service by answering weekly immigration-related questions. Here is his response from a few years back:
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Dear Mr. Lee:
In May 2000, I entered from overseas with a B-1 business visa. In November 2000, I applied for asylum based on religion. In 9/01, my application was approved. In 9/02, I can apply for the green card. My passport was issued in 9/97. It is good till 9/02.
1 Should I send the passport to the original issuing office or my country's consulate in New York for extension?
2 What will happen if I do not apply for an extension?
3 After I get the green card, can I reapply for a passport with the Consulate at New York?
4 After I get the green card, can I return to my homeland?
Dear reader:
1 Inasmuch as you have attained political asylum by stating that you are no longer under the protection of your home country, your attempt to extend that country's passport may be seen as a reflection of your true feelings that you have no fear of your home country or of returning to it.
2 Individuals who gain asylum should not apply for extensions of their country's passports.
3 Even after obtaining permanent residence in the U.S., you should not attempt to reapply for your country's passport.
4 Even after obtaining permanent residence in the U.S., you should not return to the country from which you claimed persecution. Green card holders are not afforded protections by the U.S. government, and your lack of fear in going back to your homeland could be seen to reflect upon your state of mind prior to obtaining residence status.