Unlike most tactical role-play games where a character who loses all HP are merely incapacitated for the rest of a level or feature means to recruit replacements at will, the Fire Emblem franchise features a permanent death system where a defeated allied unit are permanently lost, unable to be used in subsequent chapters. 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 and continue to appear in the story afterwards, but will still be unable to participate in battle due to their injuries. In most Fire Emblem games, with the exception of Fire Emblem: Shadow Dragon, there are only a very limited amount of recruitable characters, meaning that losing a unit can greatly hinder a player's gameplay options if they lose too many units.
Losing most units does not directly stop a chapter. 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~ where 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 to recover a lost unit. An Aum Staff, Valkyrie Staff, or Bifröst (appearing only in Ankoku Ryū to Hikari no Tsurugi, Genealogy of the Holy War, and Fates respectively) can be used to revive a character. However these staves are usually limited to one per playthrough, having usually 1 usage, and requires a high weapon proficiency with staves.
Shin Monshō no Nazo ~Hikari to Kage no Eiyū~ introduced Casual Mode which disables the permanent death feature, instead reviving defeated allies at the end of the chapter. Fire Emblem Fates introduced Phoenix Mode which revives a defeated ally at the end of the player's turn.