Runaway increases in public debt can occur for two reasons. The first is that the government recurrently spends more on goods, services and transfer payments than it receives in tax revenue.
Although the binge is unsustainable, it has the positive results that ought to flow from the expenditure on goods, services and transfer payments. It might be unwise, but the excess expenditure ought temporarily to spread a little fun.
The second is that interest on the public debt explodes. It emerges as a major item in public expenditure and indeed becomes a monster with a life of its own. One year's budget deficit adds to the public debt which increases next year's debt interest payments. Those higher debt interest payments enlarge next year's budget deficit. This in turn adds more to the public debt which raises the following year's debt interest payments.
Here the excess expenditure at no stage spreads any fun. Instead, the state has the unenviable task of raising taxes to make a show of honouring its debts, while the citizens have the disagreeable obligation of both to pay higher taxes and to save at least part of their income in government securities of uncertain future value. The uncertainty about the securities' future value arises because, by hook or by crook, spendthrift governments find ways not to repay in full what they have borrowed. The historical record — examined in Carmen Reinhart's and Kenneth Rogoff's This Time is Different (Princeton, 2009) — shows that governments find ways to cheat on the bondholders. They tax them more heavily or create an inflation that reduces the value of the debt in real terms.
Debt interest becomes a monster when the resulting loss of trust is so severe that potential investors in government debt demand a large jump in real interest rates. They demand the extra return to compensate them for the risk of possible future depredations. The change in real interest rates makes the deficits and the debt yet more difficult to sustain. It increases the debt interest charge today. Even worse, unless the government can somehow cut non-interest expenditure or extract more taxes, the increase in the real interest rate accelerates the growth of debt in future.