In privately owned corporations, when each stockholder buys a policy on each of the others, which purchase arrangement is this called?

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The situation described is a cross-purchase arrangement. In this setup, each stockholder buys life insurance on the lives of the other stockholders. If a stockholder dies, the death benefit is paid to the surviving stockholders (or to the deceased’s estate) who use those funds to buy the deceased shareholder’s shares. This keeps ownership with the surviving owners and provides liquidity to transfer the shares smoothly.

This differs from an entity purchase, where the company itself owns and is the beneficiary of the life insurance policies on the shareholders; the company uses the proceeds to buy the shares from the heirs. The other terms describe variations that involve the company as the owner/beneficiary or involve different funding mechanics, which don’t match the described arrangement where individuals insure each other’s lives.