If I defend with a character and my opponent has a deadly character attacking me and I lose, can I kill the character defending as part of the claim and avoid the deadly ? Or does deadly go off first ?

Claim is first and only then you resolves deadly.

Deadly is a passive effect. Therefore, like all passive effects, it is always initiated/resolved after settling claim during challenge resolution.

Lets see if I am explaining this right.

To elaborate just a little, it means that you could defend a MIL challenge with a character against a character with Deadly. If you lose, you could settle the claim by killing the participating killer.

Then there would be no death by Deadly.

If you choose to kill another character, then the defending guy is Deadly'd.

If you defend and lose with two against Deadly, you could settle the Claim with one, but the other would be Deadly'd.

You got it. Deadly is resolved after the claim so if no character left then deadly has nothing to kill.