The committee that designed the format of Internet mail message headers foolishly used a date-time counter. They originally provided only 2 digits for the year. In 1989 they allowed (and recommended) 4 digits. All versions of qmail produce 4-digit years.
I have reviewed my software packages and found two that read dates. My libtai library works with dates in the Gregorian calendar; it supports a range of billions of years. My mess822 library, which relies on libtai, can read dates in mail messages; it automatically converts 2-digit (and 3-digit) years into 4-digit years. A future version of qmail will use mess822 to clean up outgoing mail from ancient clients that fail to use 4-digit years.
The main threat for UNIX here is NTP, the Network Time Protocol, which counts seconds since 1900. Many NTP clients will become rather confused when the counter overflows.
My TAICLOCK protocol, which like NTP announces the current time through the network, relies on the TAI64 time format, which supports a range of hundreds of billions of years.
I offer TAI64 to the UNIX community as a replacement format for 32-bit UNIX time. Once UNIX kernels have been upgraded to support TAI64, it will be easy to upgrade applications too. The most difficult step will be conversion of 32-bit databases, such as existing filesystems, but it should be easy to complete the conversion by the year 2020.