The Roman empire was out of money when Valens became emperor. So much had been wasted by previous emperors. There was nothing left to pay Roman soldiers or even construction crews. The Roman roads were not getting repaired and soon the road network fell apart. Without the road network, food and supplies as well as soldiers could not travel quickly across the empire. The barbarians were starting to take over parts of the Roman empire. To the Romans, anyone who was not a citizen of Rome or who did not speak Latin was a barbarian.
In Europe there were five major barbarian tribes - the Huns, Franks, Vandals, Saxons, and Visigoths (Goths) - and all of them hated Rome. Each of the barbarian tribes wanted to destroy Rome. The Barbarians were destroying Roman towns and cities in the outer regions of the empire. The only reason that they had not destroyed Rome yet was they spent almost as much time fighting each other as they did Rome.
Emperor Valens had a brilliant idea. He would ally with one of the Barbarian tribes against the others. He promised the Visigoth (Goths) land, slaves and other payment if they would attack the other barbarians and keep order along the Danube River. This might have worked. It had worked in other parts of the Roman empire. But there was a big problem with the idea. Rome was broke. There was no money to pay the Visigoths for their support as Rome had promised.
The Visigoths felt betrayed by the Romans and rebelled. Although Valens was no longer emperor when Rome fell, his actions contributed to the fall of the Roman empire. Most scholars consider that the western Roman empire ended in the year 476 CE.
When the Western Roman Empire fell, it was not the end of the Eastern Roman Empire (renamed the Byzantine Empire). The Byzantine Empire continued for another one thousand years.