Stilicho's Death And The Rise of Constantius
The western empire was relatively quiet from 414-420. The years of peace, only unbroken by intermittent raids across the Rhine and other incursions, was a welcome relief from the turbulent times experienced since the ascension of Theodosius. By contrast, the east had been having trouble on their Danubian borders, as the hunnic king Rugila had been repeatedly raiding into the Balkans, causing them much trouble. No doubt Stilicho's presence in the west kept the king out of Illyricum, and strictly in Thrace. Stilicho had offered on multiple occasions to come to the aid of the east, but they were still wary of his intentions, and continued to refuse the offer.
In 415, the King of The Goths, Alaric, died of an unknown illness. It seems there was much feuding between the various Gothic nobles, and they remained fractured and disunited, different Goths supporting different nobles. The one with arguably the largest support, was the staunchly pro-Roman Saurus, with his main opponent being the brother of Alaric, Athaulf. The feuding and disunity in the Goths was just what Stilicho had been hoping for, in order to be sure they would cease to be a threat, at least for the rest of his lifetime.
How close Stilicho and Constantius were was exemplified when in 417 (the same year Constantius won the consulship), Stilicho allowed Constantine to marry Galla Placidia, essentially tying him to the House of Theodosius. It is clear Stilicho did not see him as a threat to his power, and if anything, saw him as a strong ally.
It is not known how Stilicho died, but in 420, at the age of 61, the savior of the west took his final breath. There was much mourning in the empire, and even Theodosius in Constantinople expressed his sadness at his rival's death. Honorius, without a male heir and dying, appointed Constantius as co-emperor the following year.
Shockingly, Theodosius refused to recognize this in the east. Although highly surprising, this is likely due to Constantius' association with Stilicho. It is probable that Theodosius saw a powerful general like Constantius, who was also Stilicho's right hand man, as a threat to the east. No doubt Theodosius' future actions would lend this theory some merit.