Answer: No Objectivist organization that I know of has a detailed position on nursing facilities for the aging. But here are some general principles any Objectivist would apply:
First, there is no fundamental right to health care or eldercare. Although current clients of government subsidy programs should be allowed to receive their benefits in one form or another (simply because they have based their life plans on the subsidy's existence), the government programs that currently exist should be phased out.
Insurance markets should be open and flexible, so that people can buy insurance for eldercare. This means allowing inter-state competition in insurance markets and reducing regulation. Hopefully, competition and innovation will reduce the cost of such insurance.
Although the government should not be involved in providing health care, there is no reason private charities cannot voluntarily attempt to ameliorate any shortcomings in the system that emerges. Objectivism
doesn't view charity as an important virtue, however. Objectivism
holds that each person should take responsibility for planning for the long-term needs of his life, including retirement, eldercare, and late-life medical needs.