A national government that issues its own currency and freely floats it on foreign markets never faces a risk of insolvency.
Answer: False
The answer is False.
The answer would be true if the sentence had appended the description "issues its own currency and freely floats it on foreign markets" with and only ever borrows in its own currency. The national government can always service its debts so long as these are denominated in domestic currency.
So the answer is false because if a government borrows in foreign currencies in addition to its own currency then it can clearly face a situation where its cannot get sufficient foreign currency to meet its obligations.
It also makes no significant difference for solvency whether the debt is held domestically or by foreign holders because it is serviced in the same manner in either case - by crediting bank accounts.
The situation changes when the government issues debt in a foreign-currency. Given it does not issue that currency then it is in the same situation as a private holder of foreign-currency denominated debt.
Private sector debt obligations have to be serviced out of income, asset sales, or by further borrowing. This is why long-term servicing is enhanced by productive investments and by keeping the interest rate below the overall growth rate.
Private sector debts are always subject to default risk - and should they be used to fund unwise investments, or if the interest rate is too high, private bankruptcies are the "market solution".
Only if the domestic government intervenes to take on the private sector debts does this then become a government problem. Again, however, so long as the debts are in domestic currency (and even if they are not, government can impose this condition before it takes over private debts), government can always service all domestic currency debt.
The solvency risk the private sector faces on all debt is inherited by the national government if it takes on foreign-currency denominated debt. In those circumstances it must have foreign exchange reserves to allow it to make the necessary repayments to the creditors. In times when the economy is strong and foreigners are demanding the exports of the nation, then getting access to foreign reserves is not an issue.
But when the external sector weakens the economy may find it hard accumulating foreign currency reserves and once it exhausts its stock, the risk of national government insolvency becomes real.
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