When a character's HP is lowered to 0, the character will permanently die and cannot be used in any chapter after their death. Players can lose units, but this will not cause a Game Over. However, the death of a Lord, the player's Avatar, or an important ally that needs to be protected during a chapter will cause a Game Over if they are killed. This was the set up in all Fire Emblem games prior to Fire Emblem: Shin Monshō no Nazo ~Hikari to Kage no Eiyū~ and the permanent death feature could not be disabled.
Players will need to restart the chapter (or start from the last map save or save spot in Fire Emblem: Radiant Dawn and Fire Emblem: Shadow Dragon) if the player wants recover a lost unit. An Aum Staff or Valkyrie Staff can be used to revive a character. However these staves are unique, very limited usage, and only appeared two games: Ankoku Ryū to Hikari no Tsurugi and Genealogy of the Holy War.
Certain characters in the series, such as Seth in Fire Emblem: The Sacred Stones or Frederick in Fire Emblem: Awakening, will not die in a narrative sense. They continue to appear in the story afterwards, but will still be unable to participate in battle due to their injuries.
Shin Monshō no Nazo ~Hikari to Kage no Eiyū~ introduced Casual Mode which disables the permanent death feature.