I had finished editing an audio file in Audacity, and was saving it as an MP3 back over itself (I know, that's not good), when I lost power.
The original file had been placed into a shared Dropbox folder for me. I had moved it from that folder, thereby deleting it on Dropbox, so that the one I was writing over top of was my only copy.
When power came back, I simply went to Dropbox's web site and undeleted the deleted file. I then copied (not moved) to a new folder, edited it and saved it again. Problem solved.
In related news, Dropbox announced an upcoming Android version coming in a few months, and released screenshots. There is an Android in my future, so this is good news.