Accurately identifying carotid atherosclerotic lesions at risk of rupture , which can lead to ischaemic cerebral event, is a critical clinical need. Among the proposed biomechanical indicators of plaque vulnerability, elevated stress within the fibrous cap has emerged as a key marker. However, stress predictions are influenced by several factors, including residual strains and internal stresses present even without external loads. While their existence is recognized, the quantitative and qualitative impact of residual strains on plaque stress remains insufficiently understood. To address this, we propose a Growth and Remodeling (G\&R) framework based on multiplicative kinematics to estimate patient-specific residual strains by homogenizing tissue stress. We then examine how these residual strains affect stress distributions in the atherosclerotic wall. Using CT-Angiography (CT-A) data from four patients, we reconstructed patient-specific carotid geometries and assigned heterogeneous, histology-informed material properties via an AI-driven image segmentation tool. Comparisons with purely elastic simulations revealed that accounting for residual strains could reduce peak wall stresses by up to 30\%, depending on individual morphology and tissue composition. Localized high-stress zones remained in the fibrous plaque cap, regions potentially vulnerable to rupture. High calcification leads to localized stress concentrations, limiting remodeling, whereas matrix-rich regions promote stress homogenization. In conclusion, our results suggest that incorporating residual strains in biomechanical modeling offers a more physiologically accurate view of carotid plaque mechanics. This improved representation may enhance the clinical reliability of plaque risk assessment, particularly regarding fibrous cap vulnerability. At the co-hort level, findings underscore the need for patient-specific analyses in plaque risk evaluation, reinforcing the importance of personalized biomechanical modeling in assessing atherosclerotic disease and guiding clinical decision-making.