This paper introduces a DC-link fault detection and synchronization control strategy for grid-forming inverters in hybrid DC/AC microgrids, aiming to bolster system stability and reliability. The proposed control scheme seamlessly integrates DC-link fault detection with virtual synchronous generator (VSG) control, facilitating inertia emulation and synchronization without the need for a phase-locked loop (PLL). The DC bus controller is designed to swiftly identify faults triggered by power imbalances, such as load fluctuations or generator integration, and dynamically adjust the power reference for the VSG controller to ensure inertia emulation. The Ziegler-Nichols method is utilized for meticulous tuning of the DC-link controller gains, while the modified swing equation governs VSG inertia and synchronization. MATLAB/Simulink demonstrate the superior performance of the proposed method compared to traditional GFM control strategies. Specifically, the proposed controller improved the frequency nadir to 59.98 Hz compared to 59.75 Hz and showed an enhanced power step response of 7.9×10^5 W compared to 6.9×10^5 W for conventional control method. The proposed GFM control also eliminated the 10×10^6 W switching spike observed with conventional controllers. These findings highlight the potential of this fault-controller approach to advance the reliability and efficiency of hybrid DC/AC microgrids.