IIRC War in Haven was supposed to be five chapters. As such chapter 4 will end with one of two possible outcomes.
The first outcome is the defeat of the UEF with Tev victory, but the survival of the super secret Earth project which was well hidden (most likely in the kuiper belt). As the project will result in immediate UEF victory chapter 5 will be about survivors of the Sol forces defending it until completion. In such a case we will likely see the destruction of at least one, most likely two, possibly even all three Solaris class destroyers, but I also expect them to have a lot of Tev company - they already had some 4-5 destroyers in the system and more are on their way. We may see the destruction of several of those.
The second outcome is much more mundane. The UEF successfully defends Earth but there has to be a cost to an all out Tev attack, so at least one Solaris will end up dead, but it's hard to tell which one. Tautotis is being refitted with experimental long range railguns (those use on the heavy frigates) implying that it's supposed to be used more aggressively, making it a logical casualty. Eris is guarding Mars and we know rather little about it, so it may be relatively safe. Solaris is "safely" on Earth, but since Earth is the target, I'd say Solaris is in the greatest danger. That of course implies that Steele decides to not be crafty and attack Mars to throw off Cassandra. On the Tev side I'd say a failed all-out attack on Earth will result in quite few losses, at least a destroyer or two. I'd like to point out however that BP is big on rewarding player skill. For example under normal circumstances 2/3 of the enemy warships (including Hood, a Hecate class destroyer) will simply retreat, but may be annihilated if the player is good enough. As such we may see a situation where a destroyer or two will always end up dead and two or three more may survive depending on player competence.
In both cases however I'd say Atreus is safe. Steele was brought in specifically because the previous officers were not getting the job done, and he's the driving force behind the current strategy. In fact with the emergency powers getting activated, he may be the driving force behind the entire Tev war effort. If he's dead it will be very hard, story wise, to introduce a new, engaging antagonist.