Yes, it is possible for retention-inclined interventions to irk some already dissatisfied customers to hasten their departure.
The Do Not Disturbs or Sleeping Dogs i.e. customers who are less likely to respond because they were targeted are the ones who will leave as a result of the well-intentioned interventions.
It has been repeatedly demonstrated that the very act of trying to 'save' some customers provokes them to leave. This is not hard to understand, for a key targeting criterion is usually estimated churn probability, and this is highly correlated with customer dissatisfaction. Often, it is mainly lethargy that is preventing a dissatisfied customer from actually leaving. Interventions designed with the express purpose of reducing customer loss can provide an opportunity for such dissatisfaction to crystallise, provoking or bringing forward customer departures that might otherwise have been avoided, or at least delayed.
This is especially true when intrusive contact mechanisms, such as outbound calling, are employed. Retention programmes can be made more effective and more profitable by switching the emphasis from customers with a high probability of leaving to those likely to react positively to retention activity. This paper discusses how targeting on the basis of such 'savability' can be achieved, illustrating the effectiveness of the approach with case studies. Insofar as a paper can be summarised in a motto, this paper's is "savability is the key to retention activity".