A decline in power system inertia challenges the frequency control, especially in a regional receiving-end power system. Conventionally, load shedding (LS) is the principal measure to recover the reduction in frequency. This paper proposes a two-stage frequency emergency control (EC) strategy to coordinate the LS and demand response (DR) techniques for frequency regulation to effectively and economically restore stable operation. The framework is divided into first-stage control (EC-I), second-stage control (EC-II), and coordination between EC-I and EC-II. EC-I deals with the condition when the system frequency markedly falls due to severe contingencies, with the LS approach adopted to alleviate the power-demand imbalance. Such control is devised to restore the system frequency above the set frequency index (fnadir,x) with the lowest cost. EC-II is performed based on EC-I to help the system promptly recover to a stable state. The LS and DR techniques are combined in EC-II to further reduce the control expenditure, and a control method for TCLs is proposed with less communication and computational burden to realize the power reduction. To minimize the overall control expenditure, a coordination process is designed with the coordination between EC-I and EC-II, which is reflected in the determination of the value of fnadir,x, as this parameter considerably influences expenditures in both EC-I and EC-II. The proposed framework is implemented in an IEEE 39-bus system, with simulation results demonstrating the effectiveness and economy of the strategy.