Venture capitalist David Pakman is facing a new problem lately. Many promising startups he sees as a partner at Venrock have expressed interest in raising money through cryptocurrency token sales. But if the firms do create cryptocurrencies, any investment he makes now might be undercut. “There is an argument that the equity becomes virtually worthless,” he said.

Mr. Pakman’s worry goes to the heart of an emerging debate among investors and startups about the relationship between a company’s shares and its cryptocurrency—and what rights, if any, shareholders should get up front. Concerned about potential threats to share value and regulatory risks, venture capitalists are asking for rights to receive or buy cryptocurrency in the event of an offering.