We investigated the evolution of shell structure at $N=32$ and 34 in neutron-rich nuclei beyond the stability line using realistic nuclear forces, employing the state-of-the-art valence-space in-medium similarity renormalization group method. The shell gaps are discussed from the excitation energies of the first $2^{+}$ states and the evolution of effective single-particle energies. We addressed different components of the nuclear interaction—central, spin-orbit, and tensor—and their roles in the development of shell gaps far from stability. The calculated results align well with the available experimental data and suggest a strengthening of the $N=34$ subshell gap and a weakening of the $N=32$ subshell gap below Ca. Additionally, the low-energy structures of the exotic $N=32$ isotones below Ca revealed that their ground states exhibit large deformation and coexist with a weakly deformed band at low excitation energy. The present work demonstrates essential components of the nuclear force in shaping magic numbers far from stability and provides deeper insights into the structure of exotic nuclei from the underlying nuclear forces.

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• Energy levels
• Nuclear forces
• Nuclear structure & decays
• 39 ≤ A ≤ 58