Throughout Jewish history, personal prayers have been crafted to express feelings and convey messages in a particular time and place. Some were written with a view to incorporating them into the siddur, the daily prayer book. Others were written in the format of prayers but were intended for recitation close to the hour of prayer as opposed to part of the liturgy itself, and still others were written as prayers but were meant as an emotional outlet, a form of self-expression. In the same way as a Rabbi's sermon to his congregation is based on the interaction between speaker and audience, and often includes calls to action, personal prayers written by individuals were intended as an entreaty, a plea and a cry for help from the Almighty.
During the Holocaust period, Jews composed personal prayers in which they expressed their anguish and pain before God, offering us insights into the individual suffering of many. Rabbis wrote prayers with religious significance that were usually connected to a particular event during the war; others composed prayers or poems in order to express their inner selves and their pain, without any connection to religious observance. They turned to the format of traditional prayer, finding consolation in its familiarity, this reflecting philosopher Jacques Derrida's idea of prayer for prayer's sake, as opposed to praying for the purpose of requesting something specific.
Some prayers composed during the Holocaust express despair, while others resonate with hope and resilience, depending on the circumstances in which the writers found themselves.
Many of the personal prayers written in the Holocaust did not survive. Some did, thanks to the status of the writer and the context in which the prayer was recited. Prayers recited in public by formal rabbinical leaders had a greater chance of being preserved for future generations.
Sources:
Dalia Marx, Liturgy Composed on the Brink of Catastrophe: Examination of "Akdamut Millin" by R. Meir from Worms (late 11th century) and R. Leo Baeck's Hirtenbrief for Kol Nidre service (1935), Leo Baeck - Philosophical and Rabbinical Approaches (2007), pp. 83-96
Prof. Judith Tydor Baumel-Schwartz, A Voice of Lament: The Holocaust and Prayer, Ramat Gan, 1992, pp. 11-41