The trust fund is funded by the overage of collected Social Security taxes compared to Social Security payouts. It is not "tacked on" and does not use "separate government funding".

Currently there are more payouts than taxes so the trust fund is being used to make up the difference.

When the trust fund is depleted (barring any changes, this happens at some point in the next decade if I'm not mistaken) then there will be a reckoning. If no action is taken by Congress the result is that payouts will be cut by the necessary percentage to match the taxes.