Self-regulation theory of C. Carver and M. Scheier considers goal disengagement and reengagement as an important component of effective self-regulation, closely related to sensitivity to feedback, especially negative one. Empirical studies confirm that the difficulties of changing the strategy of achieving the goal and the goal itself even with obvious negative feedback (the escalation effect) are common in the norm. The change of the goal, if it is impossible to achieve it, is linked to the better subjective well-being in the elderly. The aim of the study was to reveal the role of cognitive insight as a measure of sensitivity to feedback from others and goal reengagement in subjective well-being under different demands at work. 600 employees of the heat and power company filled the Goal Disengagement and Reengagement Scale, Beck Cognitive Insight Scale, demand-related scales of Job Demands and Resources Questionnaire, the Satisfaction With Life Scale, the Positive Affect and Negative Affect Schedule, Schaufeli’s Utrecht Work Engagement Scale and Maslach’s Emotional Burnout scale. Moderation analysis demonstrated that the interaction effects are manifested in relation to positive, but not to negative indicators of general well-being and well-being at work. The results suggest that positive emotions and work engagement are associated with greater flexibility and attention to the opinions of others. It can be assumed that a goal reengagement contributes more to positive emotions and life satisfaction in those with higher level of cognitive insight. However, the sensitivity to feedback, especially under high demands at work, should not be an expression of uncertainty and anxiety, but a manifestation of willingness to change the goal if necessary.