Rome fell, because of the immorality of the people. If a country values self seeking pleasure, mammon, sexual decadence, materialism, drugs, selfishness, and violence over anything else then it will be ruled by corruption and greedy immoral people who value and take pleasure in the same things.
This is one of the biggest misconceptions of history.
Rome did not fall due to decadence or immorality, if feel for a multitude of reasons, some of which Rome and the world in general.coubld not control.
First off natural disasters, in Peru a super volcano erupted, wiping out an entire society, it also effected the climate, the spot and ash that was sucked up into the atmosphere, was transported by weather systems across to Europe, the spot and ash would reflect the sun's rays causing the earth cool, leading to a plague virus that had lay dormant for centuries to reanimate, this virus would cause a serious plague across Asia, Africa and Europe due to trade routes, which weaken the Roman empire, which was already weaken by this point.
Which leads me to politics and empire - the Roman empire basically stretched itself to thin, they had so much land they could not control all of it, which led to wars and civil disobedience.
Immigration - because you start drooling about that term, it's not what you think, it's actually the Romans themselves who emigrated as they conquered other nations, to set up Roman systems of rule, these leaders married had children and set up routes in these nations, such as Britain and Egypt, those children grew up, had children them selves and due to this process the children and grandchildren would identify as the nation they were born in lot the nation they represented, leading to weakened systems of rule.
Famine - famines occured during the last era of the Roman empire, due to a number of factors like the volcano, weather systems ect. This would also cause civil unrest and issues which combined with the above issues.
Religion - religions changed, people adapted and evolved, a little unknown cult called Christianity was formed, many who followed it would cause rioting and would commit murder ( library of Alexandria is a famous example), societies declined due to Christianities take over and new rules, infrastructure was destroyed, bathing which was a Roman pasttime was seen as taboo and discussing due to Christianities hangups with the body, leading to disease and more plagues, meaning more death and weaker systems.
Nothing in this points to decadence leading to times fall, it's a common misconception that's peddled by conservative folks, in fact Christianities obsessions with sex and treating as a taboo evil thing, led to a decline in societal evolution, persecutions, a decline in learning and invention, death and disease, there's a reason they call it the dark ages after the Roman empire.