You have to make an educated guess.
As a last resort you can claim zero basis and claim the entire settlement as income.
Additional Answer:
You can Go online for historical stock prices For example, the historical section at Marketwatch or Nasdaq. It's generally acceptable to take the lowest and highest price from a given day and average them to arrive at a cost basis. These free services may not include events that affect basis, such as reinvested dividends, spin-offs and stock splits.
Alternatively, you could enter nothing for your cost basis, since you don't have any records and can't get any information from the stock company or the investment houses, but you would be paying more tax.
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