The 160-year-old New Melleray Abbey has been making caskets since 1999, and have a regular program for donating caskets to families in mourning specifically designed for children, according to its website.
"At our discretion, we frequently donate or discount child caskets to families," the website states.
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A spokesperson for the abbey told CNN that Green's family had reached out to them after the shooting, and the casket arrived in Tucson Wednesday morning.
"We didn't want to send an adult coffin that would be too big, we wanted something just for her," said the spokesperson.
The casket was crafted from red oak, and was made especially for Green, the spokesperson said. The lid of the casket was inscribed with her name, date of birth and death, and a cross. The family also will receive five small keepsake crosses hewn from the same wood as the casket.
The abbey's website states that they strive to produce caskets in an eco-friendly way because of a "spiritual mandate to practice responsible stewardship." They say they often make the caskets from wood taken from their own 1,200-acre forest.
"We view our casket business as a ministry - a corporal work of mercy," the website states. "We hope to impart a sense of sanctity into all that we make."