The study creates a simplified game model to propose a suitable policy to foster a win-win scenario between care institutions and families of the disabled elderly , and to give a reference basis for enhancing the welfare level of the disabled elderly as well as the commercial performance of care institutions. First, we study and synthesise the experiences of contemporary Chinese long-term care pilot cities to offer data for subsequent numerical analysis; second, we create an evolutionary game model to depict the conflicts and evolving patterns of conflicts between the disabled elderly and care facilities in China; and third, we use numerical analysis to investigate the effects of internal factors (cost of care, price of care) and policy assistance (government subsidies). Finally, we utilise numerical analysis to investigate how internal factors (cost of care, price of care) and policy assistance (government subsidy) affect the combination of solutions. The study reveals that (1) the two-sided strategic choices of care institutions and disabled families make the game unstable. (2) The government can influence the choice of care institutions and disabled families by tax rates and subsidies, implying a stability policy. (3) The presence of an evolutionary stabilization strategy implies that government control may have a desirable limit. When government engagement in this market is limited, “professional care, home care” finally becomes the evolutionary stability method.