I believe SMS messages go off into limbo, blocked at the carrier level. If she calls your number, should get a default Verizon message that you are not accepting calls from this number.
iMessage goes around Verizon and just uses Data, however you can 'block' them as well.
Delete this person as a contact, and follow the below:
In notifications, goto messages and you will see "show iMessage Alerts from". Instead of the option "Everyone", select "My Contacts Only".
So if they are not on your contact list, they cannot contact you via iMessage either.