Consider: All the kids who died at Exillium / in the Neutral Territories after being banished wouldn't have had funerals, or Wanderlings, because no one would know they were dead since they were already gone from the Lost Cities. I have this theory that Tam and Linh had a friend at Exillium who died and no one even knows. Thoughts?
This is both horrifyingly sombering and yet also very very likely. Not likely as in something that would happen within the realm of canon but likely as in if Exillium was a real place this would 100% happen.
People disappearing or going missing and no one thinks twice about it except to wonder if they're next because they're in the place people are sent to be forgotten. They aren't guaranteed another day at Exillium, which means that if they don't earn it, they're on their own. They're banished. They don't have anywhere to go, and without those check-ins with the coaches who's keeping track of them? No one.
If they don't take the bead or aren't offered one and something happens, then what? They don't have any way to contact someone, and if they do (i.e. they're a vociferator and yell really loud and someone hears or a telepath and someone is in their range) they're not exactly in the best position. They're living on their own in the neutral territories, and even though Exillium needs an address of where the kids are staying...if the kid chose to leave that spot there's nothing the coaches can do to find them. They don't have registry pendants. Kids can straight up just disappear!
With that, there would inevitably be kids dying that people don't know about. They don't know what happened to them. They were there one day and gone the next and there's no way to track them down, no way to learn what became of them. With the attitude at Exillium of trusting no one and keeping your identity secret from everyone before Sophie came along, the other waywards might not even think about it. There's the knowledge that something could happen to them, or that they aren't safe, but they were taught to be hostile towards one another; I wonder how that affects how they'd grieve, if at all. These kids might not even be grieved.
When we first meet Tam and Linh, they're very much relying only on each other, Tam speaking about not knowing how many friends you can have and Linh being more open to helping others and receiving help. So that could be paired alongside/worked into your theory about their friend. Perhaps Tam doesn't know as much because he only had the one and he lost them, so now he's even more guarded to let other people in in the future. Maybe Linh can't help but make friends with people and that more amenable attitude is what led her to be friends with both Sophie and the late Exillium friend. Linh may not have been the one to reach out, but her first response was very trusting.
All that to say my thoughts are that seems very plausible of something to have happened and I'd be curious to learn more about your theory on Tam and Linh's late friend!