The National Football League is made up of 32 franchises that are independently owned and operated according to league guidelines.
While the NFL has grown over the course of its history, no team has been relegated to a lower or alternate league.
Here's how the franchise system works in the NFL in regards to promotion and relegation.
Does the NFL have promotion and relegation?
No, the NFL is made up of 32 franchises. Each franchise was born out of an owner who bought the rights to operate a team in the league.
This closed system is different to promotion and relegation, which sees teams earn the way into (or out of) sports leagues depending on their results from each season. Instead, the NFL employs a closed system in which the teams remain the same year after year regardless of results (unless expansion or retraction were to take place).
The NFL's model is similar to that of other major North American leagues (NBA, MLB, NHL, MLS, etc.) and is considered the standard mode of operation on the continent.
Is there promotion and relegation in professional football?
Not in North America. The other professional football leagues of note (CFL, USFL, XFL) all use the closed franchise model that is the norm in North American sports.
Even the upstart Liga de Fútbol Americano Profesional in Mexico is made up of franchises, although it did have one team (Pioneros de Querétaro) that moved from a different league.