Green cards issued between 1979 and 1988 did not have expiration dates and thus, at least at present, do not need to be renewed. See the USCIS website:
Quote Quoting USCIS
Q. Do I need to renew my Green Card if it was issued between 1979 and 1988 and does not have an expiration date?

A. No. Green Cards issued between 1979 and 1988 do not have expiration dates and do not need to be renewed at this time. INS will develop an orderly plan for replacing these cards at a future time. (Note: If you obtained your Green Card before your 14th birthday and are now over 14, and your Green Card does not have an expiration date on it, you will still need to get a new card. You will need to go to your local INS District or Sub-Office—not an Application Support Center—and File a Form I-90, “Application to Replace Permanent Resident Card.” However, you will not need to pay the $130 application fee. You will only need to pay the $50 fingerprinting fee.)
(Please also take note of the notice within that document that the USCIS intends to develop a future plan for the replacement of green cards issued during that period.)

Even if your green card were expired.... Starting six months from the expiration date of a green card, you may file a Form I-90 "Application to Replace a Permanent Resident Card". Permanent residence status is not affected by the expiration of a green card, but there can be legal complications if you are in the U.S. or attempt to obtain employment without valid evidence of your status.