Imagine you have an encrypted home folder in Mac OS X 10.6 on your laptop. Now your laptop breaks down, but you were able to copy your home folder into an external hard drive from /Users/YourName which, unfortunately, holds just a YourName.sparsebundle folder.
You know your data is encrypted into that YourName.sparsebundle folder of files. Now you want to retrieve your encrypted data on your other older Mac computer, which only has Mac OS X 10.3.9 installed. You do have a Mac OS X 10.6 install disc though.
What to do?
What you'd do is find out that hdiutil on Mac OS X 10.3.9 is too old and can't open SparseBundle disk images at all, encrypted or not. The earliest version of Mac OS X that can is 10.5 according to the man pages.
The solution is to boot up your old Mac with the Mac OS X 10.6 installation disc.
If your iMac is as old as mine, it'll complain that it can't install 10.6 on that computer, but it will give you the option to restore the computer from Time Machine (or reboot).
Click on restore, which will then allow you to access the greyed out menu bar items. You'll want to select Terminal.
From there, use the Mac OS X 10.6 version of hdiutil like so:
hdiutil attach -readonly path/to/YourName.sparsebundle
It will ask you for the password, which I presume you still remember.
It will then print out some info, including the /Volume/location to where it mounted the disk image!
Then I hope you know how to use bash in the Terminal to cd to that directory, and cp -a /Volume/location /iMac/hard-drive/destination to copy recursively everything inside your encrypted home to a new unencrypted location where you can access it normally after a reboot.
Once copying is complete, just reboot the computer and remove the 10.6 install disc. You'll have your data at /iMac/hard-drive/destination or wherever you had copied it.