Depends, however generally speaking most defense firms prefer doing an examination of you prior to offering a settlement. They are able to measure your truthfulness, likeability, etc.
Herbert Tan, Esq.
The National Newark Building
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New York, New York 10007
Settlement can be discussed at any time - before, during and after a deposition. The purpose of a depositon is to get information, and pin a deponent down to their facts so they can't change their story. It also demonstrates how good a witness they'd be (and how good their lawyer is), which could either encourage settlement, or not, or not have any effect.
If you ahve your own lawyer, you need to direct this to them. If you don't yet have one, you're bets off hiring one.
PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.