This is true, but the fund is not holding a pile of cash, or stocks, or real estate investments. It's holding a pile of Treasury Bonds. The income was used to lend to the government and once expenses exceed income can only be paid out by the government buying back the bonds out of general funds. So it's really an artificial distinction.
It is more than an artificial distinction. The full faith and credit of the USG is behind the T-bills just like it is with the debt held by the Chinese or Japanese or any other holder of T-bills. The USG would have to default so as not to redeem them. If that were the case, it wouldn't really matter any more because the country would be so far gone, the economy would be in a state of collapse.