This article investigates the effect of voltage sag propagation through the transformer due to various symmetrical and asymmetrical faults in a chronological manner. A unique and precise explanation has been presented for the propagation of voltage sag through different transformer connections. The effect of voltage sag has been studied in determining the healthiness of the transformer by analyzing the parameters of insulating oil obtained through dissolved gas analysis. For this purpose, different transformer winding connections have been considered, and the analysis has been performed considering the occurrence of all major faults. In order to justify and strengthen the proposal, a real-time case study has been deliberated for depicting the correlation of propagation of fault and its effect on transformer remaining in-service period through dissolved gas analysis. The study presented in this article will help utilities to understand the voltage sag propagation along with realizing its effect on transformer healthiness, thereby ensuring total system reliability and better economical service.