I think, I've pinned possible cause of this problem, but I don't have
enough knowledge to fix it.
Here are results of "lsinitramfs initrd.img|grep ntfs>initrd.txt"
command.
For Debian 9.9:
scripts/local-bottom/ntfs_3g
scripts/local-premount/ntfs_3g
lib/modules/4.9.0-9-686/kernel/fs/ntfs
lib/modules/4.9.0-9-686/kernel/fs/ntfs/ntfs.ko
lib/i386-linux-gnu/libntfs-3g.so.871
lib/i386-linux-gnu/libntfs-3g.so.871.0.0
bin/ntfs-3g
sbin/mount.ntfs-3g
sbin/mount.ntfs
For Debian 10.0:
scripts/local-bottom/ntfs_3g
scripts/local-premount/ntfs_3g
usr/bin/ntfs-3g
usr/lib/i386-linux-gnu/libntfs-3g.so.883
usr/lib/i386-linux-gnu/libntfs-3g.so.883.0.0
usr/sbin/mount.ntfs
usr/sbin/mount.ntfs-3g
As you can see, ntfs.ko is missing in Debian 10. Problem is - I can't
add it. Just because it's missing in kernel package too. Even if I add
"echo "ntfs" >> /etc/initramfs-tools/modules" hook to live-build, it
doesn't help, simply because chroot /lib/modules/<version>/kernle/fs
doesn't have one. I guess, I need to rebuild this module from sources.
Or may be live-boot should be reconfigured somehow to support booting
via ntfs-3g, since it doesn't currently work. But I just don't have
enough experience to do it.