Rome collapsed because Romans stopped enforcing the conditions that made Roman citizenship worth anything. The same is happening to France right now.
The Western Empire's third- and fourth-century emperors, desperate for tax revenue and military manpower, settled entire Gothic and Frankish tribal confederacies inside the limes without demanding assimilation, military oaths, or any meaningful integration into Roman economic life. In 382 AD, Theodosius I settled roughly 100,000 Visigoths in the Balkans under their own chieftains, exempt from Roman law. They owed Rome nothing, and they acted accordingly. By 410, Rome fell.
The Austro-Hungarian Empire ran a version of the same experiment. Vienna absorbed millions of Slavic, Magyar, and Romanian subjects into a single fiscal and administrative unit without establishing coherent property rights or common rule of law across ethnicities. Capital fled the peripheral regions because contract enforcement varied by ethnicity and political connection. The empire spent itself policing internal tensions rather than producing anything.
Open borders can work when you couple them with private property, enforceable contracts, and zero access to a welfare state. Every historical collapse involved governments absorbing populations onto public land, public payroll, or public grain dole. Welfare states and open borders function as a single detonator, not two separate policies.