In some states, when a termination of parental rights occurs, regardless of whether there is an adoption, support ends. I don't know if KS is one of those states. As was mentioned, it may be that an adoption must occur for it to take place.
Arrears will always be due however, unless they are owed to the CP (custodial parent) and they agree to forgive them. If it is owed to the state, the NCP will always be responsible for paying anything owed to the state.
If he has recently been served, he can always deny paternity and request a paternity test. However, if the child ends up being his, he will be responsible for the cost of the testing.
Also, one can't relinquish their rights unless the other party agrees. In this case, she would need to be the one to file for termination. Like I said, it may be that KS requires an adoption before agreeing to it.
You can research KS laws at http://www.kslegislature.org/cgi-bin/statutes/index.cgi