The Donruss run is at 28 years and going, though it is divided into three parts. The first run went from 198 - 1998. There was a two year break and then another run from 2001 - 2005. Panini brought the brand back in 2014 and it has continued through 2018.
I was able to make it through the 28-year span with just four Cubs...
1981 - 1984 Bill Buckner
1985 - 1994 Ryne Sandberg
1995 - 1999 Sammy Sosa
2001 - 2005 Sammy Sosa - I was lucky here that Donruss made a card for Sammy in '05 even though he was no longer with the team
2014 - 2018 Anthony Rizzo