wget can be used to fetch a file via HTTP, and it supports -O filename.html to force the downloaded file to have that exact name. If the file exists, it is simply overwritten with the new file content.
If the request fails, the local file is empty - but that's often not desired.
The reason for this has been explained in 2006 already:
-O, as currently implemented, is simply a way to specify redirection. You can think of it as analogous to "command > file" in the shell.
The solution to this problem is to not use wget but curl:
$ curl -f http://nonexistent/file.jpg -o localfile.jpg
It will keep the current file contents if the request fails, and overwrite it if the request succeeds.