Hi @saramanning, thanks for bringing this to our attention.
If the local Dropbox folder wasn't syncing, and the files were overwritten by the site copy of the of the files, then it wouldn't be possible to recover the files from the site, since they were never uploaded there.
However, it might be possible to recover the files from the local machine from the recycle bin, or using a third party app or service to do so.
Keep me updated with any progress.