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Until about 10 years ago (during the gambling scandal and matchfixing scandal) yes, the practice was to pay for it. And in theory they could even be bought by an outsider who'd then lend it to their favourite wrestlers.
Now, I honestly have no idea how it happens (and probably nobody has, except the insiders) – in theory, they're granted by the association, but the association only approves the deals they make behind closed doors. Hakuho having "acquired" Magaki stock only involves apparently everyone having agreed that he has the right to it after he called dibs a couple months ago. I imagine they're also still traded for money, given that everyone who has bought their share before 2011 paid for it, and they'd be expected to get nothing in return – it's just not officially noted.