Can you reinitialize a hard drive without losing data?

I was in the process of copying files from hard drive A to hard drive B (both external) but the process stalled. I didn't get any messages and everything otherwise appeared to function fine, but after 10 or 15 minutes, there was no progress. The finder window said that 10 minutes were remaining the whole time and no files appeared on the destination drive. I tried quitting the process and nothing happened, so I did a force quit. Now when I connect the drive I get a message saying that the computer does not recognized the drive and would I like to initialize it? I said no. The drive does not appear in apps like DiskWarrior. Data Rescue 3 can see the drive but quick scan shows no files. I haven't tried the deep scan yet. Is the best approach to let DR3 do its thing or is there a means to reinitialize the drive without losing the data? Or is there a better app for this kind of problem?

On the hard drive are a few sparse bundle images that are password protected. I had a similar problem several years ago and was able to recover the files with DR3 but the password did not work on them. I discovered that DR3 will not recover such files that are password protected. Is there any means to recover such files?