Basis is the initial cost of something, whether it is paid by funds, loans, or both. Since you describe that the real estate is owned by the Corp (as pointed out, this is a bad arrangement),  your shareholder has no basis in the real estate owned by the corporation.

Let's not use the word Basis for the corporation/shareholder relationship for purposes of this discussion. Let's use the word Equity for "shareholder's investment in the corporation" and Liability for "the corporation owes something to someone."

1. Downpayments are part of how something is being paid for, but are not what it cost. Funds are part of Assets (money on hand), even if it is borrowed money. Using money on hand as downpayment would reduce the amount needed to borrow to cover that cost. Think of the downpayment as part of the funds being paid, but the timing is different; they didn't pay in full all at once. Paid in Advance = downpayment. Until it gets applied, it still is the corporation's funds, so it is their Asset, whether still in their bank or in the hands of the escrow company waiting on closing. Then, money (the asset) gets invested into the property (the asset); this shows you nothing has changed from the perspective of the balance sheet. That amount as Value no longer is in the form of Money; it's now Property. Basis is nowhere in this paragraph. This paragraph is just the movement of Money.

2. You didn't state if there is only this one shareholder. sjrcpa has the other part for your consideration and explanation to get the help you seek.