More precisely, there would be more jobs for such people if the government did not step in to complicate the hiring process and price potential workers out of jobs, with minimum wages set by third parties who do not, and cannot, know what the economic realities are for either the ill and the elderly or for those whom the ill and the elderly wish to hire.
Minimum wage laws in general are usually set with no real knowledge of the economic realities and alternatives for either employers or employees. Third parties are simply enabled to indulge themselves by imagining what is "fair" -- and pay no price for being wrong about the actual economic consequences.
That is why countries with minimum wage laws usually have much higher rates of unemployment than those few places where there have been no minimum wage laws, such as Switzerland or Singapore -- or the United States, before the first federal minimum wage law was passed in 1931.
Government interventions in labor markets have already created needless complications, and not just by minimum wage laws. The welfare state has already taken out of the labor market millions of people who could perform work that would be well within the capacity of inexperienced young people or people with limited education.
With welfare, such people can stay home, watch television, do drugs or whatever -- or else they can hang out in the streets, often confirming the old adage that the devil finds work for idle hands.