Find if any of the rows partially match a string

You can use LOCATE() – as in the other answer – or LIKE:

SELECT * 
FROM site_core_antispam_banned_domain
WHERE 'subdomain.com' LIKE CONCAT('%', domain_name, '%') ;

The above will look for domains that match any part of a given string. If you specifically wanted domains matching the right side of the string (for instance, if the domain to match against was somedomain.com.ro and you were only interested in *.com.ro results), you could make the pattern more specific:

SELECT * 
FROM site_core_antispam_banned_domain
WHERE 'subdomain.com' LIKE CONCAT('%', domain_name) ;

I think all you need is Locate function in MySQL as:

SELECT domain_id,domain_name as a 
FROM site_core_antispam_banned_domain 
where Locate(domain_name,'subdomain.com')!=0;

Hope this helps.

Try it:

 SELECT * 
 FROM site_core_antispam_banned_domain
 WHERE RIGHT(domain_name,10)='domain.com';