It sound like you're on the right track, that those shares with no cost basis were possibly 'sold to cover' by your employer to pay tax on the other shares you sold. Do you have a 'Supplemental Statement' from the broker that shows a cost basis for these stocks?
You could reach out to your employer to confirm this.
Here's some detailed info on Employee Stock Purchase Plans and a helpful video on How to Report Sale of ESPO and RSU stock.
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