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During the solar minimum, the Sun is perceived to be quite inactive with no spots emerging on the solar surface. Consequently, we observe a drop in the number of highly energetic events such as solar flares, coronal mass ejections (CMEs), which are closely associated with magnetic field distribution on the photosphere. However, our magneto-frictional simulations during the minimum period suggest that the solar corona could still be significantly dynamic while evolving in response to the large-scale shearing velocities on the solar surface. The non-potential evolution of the corona leads to the formation of several twisted magnetic flux rope-like structures with high magnetic helicity. These flux ropes can further be classified into two distinct groups based on their nature of progression towards probable eruptions. One set of flux ropes undergoes partial helicity shedding through reconnection with the surrounding magnetic field lines before settling down to relatively more stable structures. Another set disappears entirely, indicating a full-scale eruption. The second class can also explain the origin of occasional CMEs during the solar minimum. We also explore how other measurables such as current, open magnetic flux, free energy, coronal holes, and the horizontal component of the magnetic field on the outer model boundary vary during the evolution of these flux ropes of two different kinds. Additional analysis indicates that the speed of the outflow that mimics the solar wind can notably influence the occurrence and evolution of these flux ropes. This study emphasises the importance and necessity of understanding the dynamics of the coronal magnetic field during the solar minimum. |