Workers pay for pensions. What distinction are you trying to make?

If you have pension funds that invest on the global financial market, then pensions are being paid by workers worldwide through the companies profits. So the amount of money you get for pension can remain or even increase even if your national population collapses.

But the supply of workers needed to provide the basic goods your aging population needs (including healthcare) shrinks and if you don't accept immigrants you end up with labor shortage (Or you raise the salaries for these jobs, but then the rest of your economy disappears because there's no one working there anymore).