By writing off the debts? That's not so nice for those who are owed. A bunch of those are pension funds, for example. If peoples' pensions get wiped out by by all debts being forgiven, they won't be so happy.
By the government giving money to people? But where does the government get the money? By taking on debt? Then the government's even more deeply in debt, which means that we the people still are in debt, too.
Or does the government just create more money? This might be the least-bad way of doing it, but it would still be hugely inflationary.
But there are two things that might prevent this idea from winding up at hyperinflation. First, it is a one-off. The government prints money to pay off everyone's debt. Now nobody has debt, so the government doesn't need to do it again. Except that having no debt didn't give me enough money to buy a house, so I still have to take out a mortgage, and behold, I'm in debt again. And it didn't give my kid enough money to pay for college, so she's in debt again. And now there's cries for the government to do it again. And if they keep doing it, then we're probably going to wind up in hyperinflation. (Especially because of incentives. If the government paid off all debts, and I think they're going to do it again, my incentive is to borrow as much as I can to buy anything I think I want, because to me, it will be free.)
The second way this might not wind up in hyperinflation is because of deleveraging. A bank has $100 on deposit. They lend out $90 (fractional reserve banking), and now $190 exists, but someone owes $90, so the net is still $100. Now the government prints $90 and pays off the bank. Now $190 exists, which is no change, but the net is now $190 instead of $100, which is a change. Is that inflationary or not? I don't know.
But it's a lot easier to pay off, especially if you prioritize high risk debt to nationalize, so the government has a lower cost of borrowing (especially if the government, instead of paying off distressed debt, instead purchases it at current fair market value, since then the cost will be below the face value; “healthy” debts don't need a correction.)