Communism (in Marxism) proposes everyone should work. Does it propose people who are ill to work if they cannot?
That depends on whose definition of communism you are using.
Ferdinand Lassalle, a socialist who predates Karl Marx and the term Communism, wrote:
This credo would imply that people who do not contribute to society do not deserve to receive from society.
Karl Marx, however, criticized this philosophy in his 1875 essay Critique of the Gotha Program and coined the phrase:
That means according to Karl Marx, people should only work as much as they are able to. People who don't have the ability to contribute to society due to sickness or disability are not expected to contribute. Those who have special needs due to health problems should have those needs been taken care of by the society.
Later socialists / communists used different versions of this phrase.
Joseph Stalin wrote this into Article 12 of the constitution of The Soviet Union:
In the U.S.S.R. work is a duty and a matter of honor for every able-bodied citizen, in accordance with the principle: "He who does not work, neither shall he eat."
The principle applied in the U.S.S.R. is that of socialism: "From each according to his ability, to each according to his work."
(emphasis mine). The duty to work is restricted to "able-bodied" citizens, so anyone who isn't able-bodied isn't forced to work. However note that Marx' phrasing "according to his needs" was changed to "according to his work", which removes the duty of society to take special care of people with special needs while also justifying rewards for those who work harder than others.
Leon Trotzky was rather following Lasallee than Marx when he wrote in The Revolution Betrayed:
the distribution of life's goods in proportion to the quantity and quality of individual labor
which implies that those unable to work do not deserve to receive goods from society.