In Japan and Western Europe, where the birthrate is way below the replacement rate and immigration is either severely restricted or not well assimilated into the society, the burden of the aged rises so dramatically that their social structures might collapse under the strain.
After the Japanese Government Pension Investment Funds announced in 2009 that it would be forced to sell JGBs to meet cash requirements, it turns out that US Social Security started unloading US Government Treasuries in 2010, 6 years earlier than expected.
Of course it will take years to deplete Japanese or American pension funds, but the switch from being net buyers of government debt to net sellers makes a hell of a difference. First, it finally makes it clear beyond any doubt that the entitlement system is not sustainable and will get worse over time. Second it will push upward pressure on government debt yields, as major buyers of debt not only stop buying, but start selling.