Apart from a number of Imperial provinces we haven't yet visited or seen in Ilsabard, there isn't actually "lost remnants" stationed beyond Eorzea, because the Empire never got beyond Aldernard due to Gaius continuously failing to subjugate the realm (the only other Imperial provinces were in Othard and, well, we've liberated those). There has been lots of headcanons about some being in Tural, but that is just based on vague assumptions with no basis in fact (until SE proves otherwise).

I know it's a bitter pill to swallow, but it's clear the Empire is now dead - slain by it's own hand and now lying in state in it's black ashen shroud - just like it's creator wanted, ironically. Certainly Garlemald will rebuild as the survivors of the civil war and the Telephori's tempering come together with the Alliance's assistance, but with a new non Imperial government decided by it's people.