Rarely bad and never woeful
In the 1960s, the Pittsburgh Steelers were a really bad team. Woefully bad. Then Chuck Noll took over.
Things did not improve improve immediately. They went 1-13 in 1969 and had losing records the next two years. But 1969 was the last year the Steelers failed to win at least five games in the regular season.
That's a fairly impressive record. The other dynasties cannot match it. Dallas sucked in 1988 and 1989 (only four wins in the two years combined). The Patriots had a horrible year in 1992 (two wins). The 49ers only won six games total in the 2004 and 2005 season.
Only one other NFL team can match the Steelers on this score. Denver only won four games in 1971 but that was in a fourteen game season and they had one tie. You have to go back to 1967 to find a woefully bad Broncos team.
I think this record says something about the quality of the ownership of those two teams. Both have consistently fielded playoff teams (and won Super Bowls) without ever dropping into the league's cellar.
There is, after all, a benefit to being occasionally woeful in the NFL. A really bad team gets the best draft position. The Colts "won" Peyton Manning by going 3-13. The prize the Cowboys got for their bad streak was Troy Aikman. Teams like Pittsburgh and Denver never receive that bonus. Yet, somehow, they keep operating at the top the league.