Who is saying that people shouldn't be paid? Either you've completely missed the point or you're deliberately trying to obfuscate the conversation because for some reason you love living in our current late stage capitalist hellscape.
I don't think anybody has expressed an opinion that people shouldn't be paid, or that they should work for free, or that there should be no goods and services available on an open market. You seem to be arguing with an imaginary adversary of your own invention.
What several PP have expressed is that essential goods and services (food, housing, water, utilities, education, healthcare etc) should be not-for-profit, or more specifically that there should be a not-for-profit option available, with the private market existing to provide uplifted goods and services for those who want them. Not-for-profit doesn't mean free, and it doesn't mean the people working in those industries shouldn't be paid. In actual fact, the hope would very much be that the actual workers and producers in these industries would receive a fairer compensation package without the need for both workers and consumers/service users to sacrifice wealth and productivity to billionaire corporate entities.
So your friend wouldn't need to rent a house to pay for her mother's care (remember that the vast majority of this money simply goes straight into the pocket of the wealthy private care home owner) because the state would provide a quality care service where the staff are well paid and well trained. If she wanted to rent her home for profit, then she would be competing with excellent and affordable social housing rentals, so she would need to actually add some value that people were willing to pay her in inflated sum for, such as a particular location or luxury standard accommodation.
Ditto the supermarkets. If we had Great British Grocery Stores that sold goods produced fairly in the UK and sold to the consumer at cost price, where everybody was free to shop for basic staple items, there is no reason why supermarkets could not exist alongside this. But again, they would need to actually provide something that people were willing to pay extra for, such as luxury or niche items. No longer would they be able to cream off multi billion pound profits by screwing suppliers and overcharging customers for basics.