Only if you're using a backup system. Backblaze and Dropbox can recover previous versions of a file even if the new file has been backed up. There are programs that can recover deleted files, but I don't remember ever having a successful recovery.
When a file is deleted your computer just rewrites the directory on your drive to say the place where the file was saved is now empty. The data itself might still be there, at least until something is written over it. File recovery software scans your drive looking for intact files in the writable areas if the drive.