Where there is no written contract, the parties are entitled to try to prove the terms of the contract in court. Where no terms can be ascertained directly from the evidence, the court can "imply" the existence of a contract from the parties' respective conduct.
Your stated facts could indicate that you were merely the editor and publisher of the other party's book, or that the two of you were partners with a joint interest in the outcome of the work, and joint liability for the costs.
If you were merely an editor/publisher, then your obligation would be to do a competent job -- in which case, your errors could be viewed as negligence and you could be held liable for the resulting losses that would be required from having to produce a second printing after re-editing the project.
Conversely, if you are partners, then you would have a claim against your partner for one half of the printing costs, and joint liability for any errors in the printing.
A third theory would be that you never agreed to edit, but only to publish the book, so the typos are not your responsibility at all.
The first of the above-described theories would leave you liable for the entire cost of the printing, the second for one half, and the third for nothing. Which one you should use to defend yourself depends entirely on the virtual "paper trail" that you've described. You need to examine that trail objectively and pretend that you are the judge, you know nothing about the parties before you, and then try to decide from what you have, which theory is the most likely.
This is what the judge will do, and it will give you the best answer about how to potentially settle the matter before court and how to set forth your argument to the judge, if you cannot resolve your dispute before trial.
Hope this helps.
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