Rescue data from a Mac that won't start anymore

My wifes macbook didn't start anymore, it tried but went into the same error again and again. This is how I got the data from the old hard drive.

1. Get yourself a drive to rescue the files to (we will call it LIFEBOAT). Connect it to the mac.
2. Enter Recovery mode by pressing CMD and R at startup.
3. Get yourself a terminal (in the upper menu under "Utilities").
4. Make sure LIFEBOAT can be found under /Volumes/LIFEBOAT.
5. Make sure your userdata is in /Volumes/Macintosh HD/Users/YOURUSERNAME.
6. Copy the files you need to the LIFEBOAT with a simple cp -r command.
7. Close the Terminal (CMD-Q) and shut down the Mac.

The critical step is clearly step 5. If the data is not there, I have no idea what to do.

The mac I used was running an old version of OSX (Mavericks) and I think in the newer ones the files might be encrypted.

I did have two backup plans:

• Try to find whatever is left from the files with TestDisk, perhaps after copying the drive to make sure I don't destroy anything by excident. This was a recommendation of Pascal and David.
• Pay someone to rescue as much data as possible. There are companies for this.

In the end I was very glad to get everything back.