Or use a domain alias. Some control panels let you do this, otherwise it needs to be done in the apache configuration.
Basically, you need both domains on the same server. Next make sure you delete the subdomain "subdomain.abc.com", that way it won't get mixed up with the new alias. Note you will still need "subdomain.abc.com" in your DNS entries.
Next add an alias for that domain in your httpd.conf. The first two lines of the virtual host section for that subdomain will look like this:
Or similar. Add a space then "subdomain.abc.com" on the second line. Once your done reload apache and its finished. Everyone who goes to subdomain.abc.com will see the same information as if they went to clients.xyz.com.