I don't think Champions should die (at least in combat) ...
But I think you should CAPTURE champions when you win in combat (only if you ALSO have a champion in your army ... aka if a champ beats a champ, they make a capture, but if Soldiers beat Champ, champ runs away. Sov always escapes).
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That way, once you capture the Champion, you can either release him (+Valor), set him up for ransom (neutral ... imprisoned until ransom is paid), or imprison for the purpose of torture (+Dread).
Basically you can release him immediately, or you can imprison him in a city of your choice (unmovable, gets freed if that city is captured by ANYTHING OR ANYONE).
Once the Champion is imprisoned, you can post a ransom at any time, though you don't have to. And even if you post a ransom you can still have a dread-inclined champion to sit in the city with him (torturing him) to gain dread.
Once a Champion has gained enough dread (and you have a city with either Gallows or Guillotine) you can choose to publicly execute a prisoner instead.
Once you can execute Champions, you can put them in a "threat of death" which gives a low % chance (10-15) of converting the Champ and a high % chance of killing them (without increased dread, because of the conversion chance)
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However, if a Champion has high Valor, he can talk with a Champion to try and convert them (20-30% chance). This can only happen once per prisoner, as the prisoner is released either way (either they join you, or you release them).
This chance is doubled if the champion is opposite alignment of their current liege, or if their current liege is dead (faction destroyed).
Also a slight increase to conversion chance if the champion is of different race (culture) than liege but same race as the initiating (high valor) champion.
Other than that, normal 'release of prisoners' increases valor, while torture, and normal executions increase dread. (normal as in without a chance of champion conversion).
Threat of death conversions will always have the same low percentage chance however ... unless somehow they are philosophically aligned with the threatener (same alignment AND similar level of dread)
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Champions (without a Faction) that are released will be placed in a newly formed Quest item (somewhere on the map).
While a PRISONER won't die if their Faction is destroyed, as they can still be tortured, executed, or death threat/ valor converted.
However, a released Champion without a faction that is initiated in combat (and defeated) will die forever as normal ... aka newly found champions.