/usr/share/initramfs-tools/scripts/casper-helpers is in casper 1.340.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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if [ "${BUILD_SYSTEM}" = "Debian" ] || [ "${BUILD_SYSTEM}" = "Ubuntu" ]; then
    MP_QUIET="-q"
else
    MP_QUIET=""
fi
if [ ! -x "/bin/fstype" ]; then
    # klibc not in path -> not in initramfs
    export PATH="${PATH}:/usr/lib/klibc/bin"
fi
sys2dev() {
    sysdev=${1#/sys}
    echo "/dev/$(udevadm info -q name -p ${sysdev} 2>/dev/null|| echo ${sysdev##*/})"
}
subdevices() {
    sysblock=$1
    r=""
    for dev in "${sysblock}" "${sysblock}"/*; do
        if [ -e "${dev}/dev" ]; then
            r="${r} ${dev}"
        fi
    done
    echo ${r}
}
is_supported_fs () {
    # FIXME: do something better like the scan of supported filesystems
    fstype="${1}"
    case ${fstype} in
        vfat|iso9660|udf|ext2|ext3|ext4|btrfs|ntfs)
            return 0
            ;;
    esac
    return 1
}
get_fstype() {
    local FSTYPE
    local FSSIZE
    eval $(fstype < $1)
    if [ "$FSTYPE" != "unknown" ]; then
        echo $FSTYPE
        return 0
    fi
    /sbin/blkid -s TYPE -o value $1 2>/dev/null
}
where_is_mounted() {
    device=$1
    if grep -q "^$device " /proc/mounts; then
        mountpoint="$(grep "^$device " /proc/mounts | awk '{print $2; exit}')"
        grep "^$device " /proc/mounts | read d mountpoint rest
        echo $mountpoint
        return 0
    fi
    return 1
}
lastline() {
    while read lines ; do
        line=${lines}
    done
    echo "${line}"
}
base_path ()
{
    testpath="${1}"
    mounts="$(awk '{print $2}' /proc/mounts)"
    testpath="$(busybox realpath ${testpath})"
    while true ; do
        if echo "${mounts}" | grep -qs "^${testpath}" ; then
            set -- `echo "${mounts}" | grep "^${testpath}" | lastline`
            echo ${1}
            break
        else
            testpath=`dirname $testpath`
        fi
    done
}
fs_size ()
{
    # Returns used/free fs kbytes + 5% more
    # You could pass a block device as $1 or the mount point as $2
    dev="${1}"
    mountp="${2}"
    used="${3}"
    if [ -z "${mountp}" ]; then
        mountp=$(where_is_mounted "${dev}")
        if [ "$?" -gt 0 ]; then
            mountp="/mnt/tmp_fs_size"
            mkdir -p "${mountp}"
            mount -t $(get_fstype "${dev}") -o ro "${dev}" "${mountp}"
            doumount=1
        fi
    fi
    if [ "${used}" = "used" ]; then
        size=$(du -ks ${mountp} | cut -f1)
        size=$(expr ${size} + ${size} / 20 ) # FIXME: 5% more to be sure
    else
        # free space
        size="$(df -k | grep -s ${mountp} | awk '{print $4}')"
    fi
    if [ -n "${doumount}" ]; then
        umount "${mountp}"
        rmdir "${mountp}"
    fi
    echo "${size}"
}
setup_loop() {
    local fspath=$1
    local module=$2
    local pattern=$3
    local offset=$4
    modprobe ${MP_QUIET} -b "$module"
    udevadm settle
    if [ "$module" = loop ]; then
        if [ ! -e /dev/loop0 ]; then
            # temporary workaround for kernel bug
            for i in 0 1 2 3 4 5 6 7; do
                mknod "/dev/loop$i" b 7 "$i" || true
            done
        fi
        dev="$(losetup -f)"
        if [ "$dev" ]; then
            if [ -n "$offset" ]; then
                losetup -o "$offset" "$dev" "$fspath"
            else
                losetup "$dev" "$fspath"
            fi
            echo "$dev"
            return 0
        else
            panic "No loop devices available"
        fi
    else
        for loopdev in $pattern; do
            if [ "$(cat $loopdev/size)" -eq 0 ]; then
                dev=$(sys2dev "${loopdev}")
                if [ -n "$offset" ]; then
                    losetup -o "$offset" "$dev" "$fspath"
                else
                    losetup "$dev" "$fspath"
                fi
                echo "$dev"
                return 0
            fi
        done
        panic "No loop devices available"
    fi
}
# Returns 0 on success
# panics if remount- or bind-mount fails
# returns 1 on failure otherwise
try_mount ()
{
    dev="${1}"
    mountp="${2}"
    opts="${3}"
    if where_is_mounted ${dev} > /dev/null; then
        if [ "${opts}" != "ro" ]; then
            mount -o remount,"${opts}" ${dev} $(where_is_mounted ${dev}) || panic "Remounting failed"
            return 0
        fi
        mount -o bind $(where_is_mounted ${dev}) ${mountp} || panic "Cannot bind-mount"
        return 0
    else
        mount -t $(get_fstype "${dev}") -o "${opts}" "${dev}" "${mountp}"
        ret=$?
        if [ $ret -ne 0 ]; then
            log_warning_msg "Cannot mount ${dev} on ${mountp}"
            return 1
        fi
        return 0
    fi
}
find_cow_device() {
    pers_label="${1}"
    cow_backing="/${pers_label}-backing"
    if [ -z "${PERSISTENT_PATH}" ]; then
        pers_fpath=${pers_label}
    else
        pers_fpath=${PERSISTENT_PATH}/${pers_label}
    fi
    for sysblock in $(echo /sys/block/* | tr ' ' '\n' | grep -v loop); do
	# do not ever probe floppies, probing nonexistant ones delays the boot to half an hour and longer
        n=${sysblock##*/}
        if [ "${n#fd}" != "$n" ]; then
            continue
        fi
        for dev in $(subdevices "${sysblock}"); do
            devname=$(sys2dev "${dev}")
            if [ "$(/sbin/blkid -s LABEL -o value $devname 2>/dev/null)" = "${pers_label}" ]; then
                echo "$devname"
                return
            # Do not add any filesystem types here that might be able to
            # mount a journalled filesystem and replay the journal. Doing so
            # will cause data loss when a live CD is booted on a system
            # where filesystems are in use by hibernated operating systems.
            elif [ "$(get_fstype ${devname})" = "vfat" ]; then
                mkdir -p "${cow_backing}"
                try_mount "${devname}" "${cow_backing}" "rw" || continue
                cow_backing_mp=$(where_is_mounted "${devname}")
                if [ -e "${cow_backing_mp}/${pers_fpath}" ]; then
                    echo $(setup_loop "${cow_backing_mp}/${pers_fpath}" "loop" "/sys/block/loop*")
                    return 0
                else
                    umount ${cow_backing_mp}
                fi
            fi
        done
    done
}
find_files()
# return the first of $filenames found on vfat and ext2 devices
# FIXME: merge with above function
{
    filenames="${1}"
    snap_backing="/snap-backing"
    for sysblock in $(echo /sys/block/* | tr ' ' '\n' | grep -v loop); do
        for dev in $(subdevices "${sysblock}"); do
            devname=$(sys2dev "${dev}")
            devfstype="$(get_fstype ${devname})"
            if [ "${devfstype}" = "vfat" ] ||  [ "${devfstype}" = "ext2" ] ; then # FIXME: all supported block devices should be scanned
                mkdir -p "${snap_backing}"
                try_mount "${devname}" "${snap_backing}" "ro" || continue
                for filename in ${filenames}; do
                    if [ -e "${snap_backing}/${filename}" ]; then
                        echo "${devname} ${snap_backing} ${filename}"
                        return 0
                    fi
                done
                umount ${snap_backing}
            fi
        done
    done
}
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