As grid-connected converters are at risk of losing synchronism with the grid when exposed to extreme voltage sags, this might jeopardize the stability during a fault and a converter's ability to comply with fault ride-through requirements. This paper investigates the synchronization stability of grid-tied converters during severe symmetrical faults with phase jumps. To achieve zero-voltage ride-through capability, a frozen PLL structure can be employed to guarantee stability during faults. However, as the frozen PLL approach is unaware of frequency drifts and phase-angle jumps in the grid voltage, its performance during non-constant frequency and phase is unknown. Therefore, this paper investigates and provides new insight into how the frozen PLL performs during phase jumps and reveals whether phase compensation should be utilized to improve the converter response during a severe symmetrical fault. It is disclosed, that even though phase compensation can improve the injected currents during a fault situation including large phase jumps, a non-compensated frozen PLL can inherently ensure stability and allow for zero-voltage ride-through capability at an acceptable current injection. Furthermore, the robustness of the frozen PLL has been analyzed through a comprehensive simulation study where three test cases have been experimentally verified, which confirms the presented findings.