What do you do after ddrescue finishes?
OK, after more research I'm going to try to answer my own question. Apparently if you use ddrescue it doesn't automatically create a drive image unless you tell it to produce a specific file, say mydrive.img
within the drive to which you are writing (the target).
Once you've done that you can use something like lzip or lziprescue to extract the actual directories and files you're looking for.
However, I'm still unclear as to whether you can rescue an individual directory within the failing drive or you have to rescue the whole partition. If I can figure that out I'll add it to this answer.
Also you might have to perform more operations on the image file before you can extract its files, but I don't know what you'd use to do that.