"subsequent handling of" means "how to handle the message next"... like "do I mark this as spam or deliver it to the inbox". That's how I understood it.

In any case, the fact that we're talking about it means this content needs to be made more clear! How about:

Email service providers can use the DKIM signature to decide what to do with an incoming email. For example, if the DKIM signature fails because it doesn't match the sending domain's DNS records, the email could be dropped, quarantined, or delivered with a warning message. Service providers can also use the signature verification in anti-spam systems.

^ I don't think we need to include all the nitty gritty details.