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Not at all, it depends on the residence permit. With a C permit you can buy and rent properties, while with B you can buy only your own home

Not quite. If you reside in Switzerland, you can own rental homes. Just foreign non-residents cannot buy.

Can you go into more detail?

This only affects homeowners who live in their own property, not landlords. If you earn rent on your property, you will still pay income tax on it.