Response cost is a term used in Applied Behavior Analysis for what we more generally call consequences. It is removing a reinforcer because of an undesired or inappropriate behavior. It is a form of punishment. If a child breaks a particular rule he or she may lose a token (from a token system) or points. In some cases, the child might actually lose a field trip or other earned reward.
In some school districts or private institutions, response cost is not permitted. It can be used by teachers or staff in a vindictive manner that can make reinforcement ineffective. Like all punishment, it may only make the inappropriate or unacceptable behavior disappear when the punisher is present. It may reappear out of that person's presence.
Still, with some student's I have found response cost can be effective. I address the challenges in my article, but the use of response cost has to be case by case. Differentiated reinforcement can sometimes be effective. As a practitioner, you have to base your judgement on the danger of the inappropriate behavior (such as eloping) and whether response cost decreases the target behavior as well as reducing the inappropriate behavior.