"It isn't fair to give a new use for some one else's hard labor" is the capitalist idea of fairness. The communist idea of fairness is "From each according to his ability, to each according to his needs" (Karl Marx: Critique of the Gotha Program).
In Communist theory, the communist worker wouldn't build a home for themselves. They would build a home for the community. The community would then give that house to the person in most need of a new home. Also, a communist worker who finds a new and original way to improves his hammer and sickle so he can work more efficiently wouldn't keep it for himself. He would switch his profession to "tool improver" and use his newfound ability to improve the tools of all other workers.
In Communism, private ownership of any subjects of labor and any means of labor are abolished. Subjects of labor are any raw materials which can be turned into more valuable goods. MeansAll products of labor are any tools, machines or real estate properties which have the primary purpose to do that. The end-products are then distributed by the community following the Marxist doctrine of "to each according to his needs". So the community would then give that house to the person in most need of a new home.
Most forms of communism differentiate between private property and personal property. Ownership of personal property is protected while private property is to be abolished. Friedrich Engels and Karl Marx wrote in Chapter II of the Communist Manifesto: "The distinguishing feature of Communism is not the abolition of property generally, but the abolition of bourgeois property". Andreas Berkmann clarified what exactly that means in Now and After: The ABC of Communist Anarchism: "The revolution abolishes private ownership of the means of production and distribution, and with it goes capitalistic business. Personal possession remains only in the things you use, Thus, your watch is your own, but the watch factory belongs to the people". However, that line can be blurry. Different interpretations of communism have different ideas where the separation between personal property and communal property should happen.
Depending on how your branch of communism interprets personal property, the house would then either become personal property of that citizen or just considered a temporary lend by the community.