Captain America once died in the comic books in the aftermath of Marvel's "Civil War" comic event. With the MCU's own Civil War out of the way, and with him technically a criminal in the eyes of the United States government, Rogers is at a very troubling point in his life right now.
Captain America dying would send shockwaves throughout the MCU, but it would be the ultimate motivation for the rest of the Avengers in the battle against Thanos.
In the comic books, when Rogers originally dies, Bucky takes his place as Captain America until, in true comic book fashion, Rogers is revived. In a later, separate story arc, Sam Wilson a.k.a. The Falcon (played by Anthony Mackie in the MCU) becomes Captain America. Both have been set up as loyal allies to Captain America in the films who would be worthy replacements.