Q. What if I don't know the giver's (donor's) cost basis?
A. You have to report the sale on your tax return. Lacking any cost basis, the IRS will consider the entire sale amount as taxable. So, you need to make your best effort to determine the original cost basis, even if (worst case) it's a guess. Historical prices of publicly traded stocks are readily available on the internet and should, at least, satisfy the IRS that your basis wasn't zero; just "google" “Historical Stock Prices". I use http://bigcharts.marketwatch.com/historical/. The stockholder relations dept. at the company may be able to help.
Unknown Basis
https://ttlc.intuit.com/community/investments/help/how-do-i-find-a-stock-s-cost-basis/00/25750
