if I have a ruined rex defending against akali silent with 8 might, and I have a karthus at my base, how will this resolve?

Yes — Karthus makes Ruined Rex's Deathknell fire twice, and both triggers can hit Akali, killing her.

Here's the sequence: Akali (8 Might) and Ruined Rex (6 Might) trade combat damage. Rex takes lethal and dies; Akali takes 6 (non-lethal). Combat Cleanup then heals Akali, and she isn't recalled because no Defenders remain — but she keeps her Attacker designation until Combat ends (Rule 466.7). Rex's Deathknell triggers twice since Karthus is on the board (his passive works from Base), creating two separate 4-damage chain items. Those triggers resolve before Combat ends (Rule 466.2; FAQ #10444), so Akali is still "in combat" and her "can't be chosen unless in combat" protection does not apply. Both triggers can target her: 4 + 4 = 8 damage equals her Might, so she dies.