The paper examines potential costs to the self-concept of attachment avoidance. Avoidant individuals experience low self-concept clarity, in part because they do not receive self-verification from their romantic partners.
Emery, L. F., Gardner, W. L., Carswell, K. L., & Finkel, E. J. (in press). You can’t see the real me: Attachment avoidance, self-verification, and self-concept clarity. Personality and Social Psychology Bulletin.