setuid without execute bit
 

setuid bit allows the process to execute the file with the uid of the file. But, what is the purpose of setting setuid without execute bit?

The man page tells that if a file is setuid without execute flag, the permission will be displayed as 'S' (capital s) in ls command. Why should anyone set the setuid without execute flag?

Does setting setuid without execute flag have any special meaning?

I would think it is just a case of orthogonality, of every combination being available. The 'S' is just so you know the x bit is not set. Likewise, you can have rwx bits all off - it isn't particularly useful, but you can do it.

Conceivably there might be a scenario where you don't want the owner to accidentally execute the setuid file. This doesn't prevent group class users and other users executing it, assuming the other execute bits are on. But it would be an obscure case.