The above is a great answer.

To expand on this (from some googling). All of this requires root.

1) Create a sparse file (actual size depends on usage)

  truncate -s 100G /home/zzz/Dropbox.image

2) Create a ext4 filesystem on it

  mkfs.ext4 -m0 /home/zzz/Dropbox.image

3) Mount it as a loopback file system

  sudo mount /home/zzz/Dropbox.image /home/zzz/Dropbox-fs

4) Create / Copy your dropbox folder to Dropbox-fs

  sudo mkdir /home/zzz/Dropbox-fs/Dropbox
  sudo chown -R zzz.zzz /home/zzz/Dropbox-fs/Dropbox
  cp -r /home/zzz/Dropbox-original /home/zzz/Dropbox-fs/Dropbox

5) Start Dropbox and point it to the new location

6) If we want to mount this automatically at login. Adding it to /etc/fstab may not work because of encryption.

But perhaps some script at login to mount it will work. For example, we can create a script at /usr/local/bin/mountDB.sh and then add a line to /etc/sudoers

  zzz ALL=(root) NOPASSWD: /usr/local/bin/mountDB.sh

Then somehow call this script at login of user zzz.