How will Western civilization end? — through the end of its people. How will that happen? If history is a guide, through internal collapse and outbreeding, probably simultaneously.
Internal collapse will come from dysgenics, or the rewarding of sustenance to those who could not achieve it on their own, leading to a gradual prevalence of less adapted traits over the more adapted. This occurs because civilization changes the index of adaptation from reality/nature at large to human social rules.
The crisis of dysgenics is not solely that the less adapted breed. It is that as these accelerate in ratio, the more-adapted find life increasingly tedious, frustrating and moronic, and so they tend to self-destruct or at least, not reproduce. It is a fitting revenge in that they are able to destroy civilization this way, a parting shot of hatred for the misery it forced upon them.
Outbreeding is the other threat. This generally occurs through trace admixture. Someone from another population who is 0.05% Other, for example, will breed into the population, followed by many more. Soon that percentage of Other creeps upward as the more recessive traits of the population are suppressed. Eventually the population is a shadow of itself.
In the West, the most likely doom is assimilation by Asiatics. First, trace admixture through groups with Asiatic admixture — Southern and Eastern Europeans — will remove the Western nature of the population. At that point, it will assemble itself by convenience for business and social functions, and more will take on foreign wives.
Simultaneously, the dysgenic influence will lower the capabilities of the native group, making it on par with other foreign groups. At this point, there will be no barriers to miscegenation and the group will hybridize. The end result will be mostly Caucasian, but will visually and intellectually more resemble the Asian and middle eastern elements bred into it.
This is genocide by another form, but it is brought on by decay from within, starting with the breeding of less-adapted because they are able to survive in social situations that, by their unrealistic and trivial nature, drive the more-adapted to cease breeding.
This process has happened many times through history and no ethnic group has recovered from it.