When booting the Alpine Linux installer ISO, the modloop is directly loop-mounted from it and prevents the umounting of it. Just umounting the modloop results in the kernel modules being inaccessible.

This is a quick cheatsheet how to copy the modloop into ram:

First, find the path of the modloop:

localhost:~# losetup -a
/dev/loop0: 0 /media/sdb/boot/modloop-vanilla

Copy it into the rootfs, which is in RAM:

cp /media/sdb/boot/modloop-vanilla /

Umount the disk-backed modloop:

umount /dev/loop0

And mount the copy in RAM in its place:

mount -o loop /modloop-vanilla /.modloop

Finally, umount the boot disk:

umount /media/sdb