A special legal entity is created for each deal. In the US, such legal entities are called special purpose vehicles (SPVs). 100% of an SPV’s authorized capital consists of the acquired shares of the investees.
The SPV acts as a "wholesale" buyer of the company's shares. The investor buys a share in the SPV proportionally to how much of the final asset they own in the SPV’s authorized capital.
The powers of the manager
The syndicate manager is authorized to sell shares and distribute income to the SPV shareholders when the investment is complete.
The manager cannot use the SPV for any other purpose, sell or pledge shares, dilute capital, etc., without the consent of the participating investors.
The SPVs are registered in Delaware because Delaware law is best suited for the venture capital business. The state has a developed practice in the area of venture capital investments; its standard terminology, template documents and case law make enforcement easier and cheaper there than anywhere else in the US or the world.
99% of all US startups are registered in Delaware, and venture capital firms also prefer to register companies and transactions there.
The State of Delaware offers foreign investors zero capital gains tax, which creates a unique environment for investing in the US economy.