Technically, Jack owned the house and his basis would be the basis his mother had when the house was acquired, plus the cost of improvements. However, since he only paid $1 for the house, in essence he wasn't the real owner so it is possible the IRS would treat the house as an inheritance to the siblings upon her demise, in which case the basis of the house would be its fair market value at that time. If so, the conservative thing to do for the siblings would be to report their share of the proceeds as the sale price of inherited property and the cost basis would be the fair market value of the property when the mother died, plus the cost of improvements after that point in time.
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