'the means of production owned by the workers’

is socialism

Under that system, if your body loses its ability to work you would also lose your right to own the means of production, right?

No.
Under both socialism and communism it’s “from each according to their ability, to each according to their needs” (like, it’s literally in the names - social, commune they’re literally about making sure all of society, all of the community, are cared for), communism doesn’t even have money, and all basic needs are met, so there is no need to sell your labour in the first place.

Communism, especially as you have it defined here, is not the only alternative to what’s being described in the photo. It’s not actually giving a solution, just defining a problem with capitalism.

Do you mean Leninist communism? There are a lot of different types of communism. What the Soviet Union did was only one type.