A country defaulting is more akin to a bank running out of money than a person defaulting.
A country is financed in several ways, and is kind of like a stock market to use a crude example. Countries invest in treasury bonds because it is a good safe return. For example, other countries may buy US bonds because they know that for every dollar they put in, seven years later they'll get it back in double. The same goes for businesses, and 401ks for company employees, and banks as well.
Now, keep in mind that the United State's economy is propped up by the housing market. When people buy a house, they suddenly have all these new expenditures that really keeps the economy flowing. You need to buy lamps, couches, paint, wallpaper, hire construction workers to open up a wall, fertilizer, tvs, etc etc etc on top of things like property tax, and mortgage.
Now, the banks typically lend money to the home-buyer and in return they earn a good interest rate on it while at the same time supporting the principles of John Nash's economics (the best decisions involve what is best for both the individual and society). This is where the practices of the ARMs (adjustable rate mortgage startups went wrong. They did what's best for themselves at the expense of society and tanked the country).
Banks have two primary ways of making money. Investments in stocks/bonds, and interest from lending.
And in order to decide what kind of risks they are willing to take, they have to keep in mind the relative security of their own investments.
Bank A knows that they have 320million in income this year, some of it from bond maturity. They can afford to lend out a portion of that, and then reinvest the rest in stock and bonds. This then helps them loan out money through which they earn more interest.
On a larger scale, different countries also invest in OTHER country's bond markets because for one reason or another, the return is better. So, say, Greece for example may buy 500m every year in American bonds, and earn a billion back.
A country may also buy it's own bonds as well. What this does is directly inject liquidity into the banks. If US injects 1 B, the banks can immediately start lending around 75% of that, and typically invest the rest. That 750m is lent out, and the funded people use that to buy houses or cars etc etc, and the companies that sold those products then invest those earnings back into the bank, where the bank then loans it out again in diminishing returns.
This can result in 5B in new investments from the original 1B.
It is similar to welfare (which is why I have no idea why people are against it when it's been shown that the gov makes $1.60 for every dollar they put into welfare through a similar diminishing inevestment/return process as above.)
Now, after all that, imagine what happens when said lending country defaults. Suddenly, the banks who thought they had 800m in returns now have 90million, can't afford to loan out any money, now must invest in less ideal bonds with less return in a different country. People with 401ks suddenly have 600k from the 1m they've invested over their lifetime, have to start being more conservative, spending less. Companies make less and invest less, resulting in banks earning less interest and liquidity, etc etc etc
Now, compared to the typical citizen where there is a completely outlined process for default and there are creditors and credit ratings and collections and they can just take your property and sell it.
However, with countries, there is no real international guideline or process. With hundreds of thousands of people having defaulted, there's been room to critically analyze the process and improve it to the point where it's a relatively easy transition.
When this happens to a country, really any country that has invested in said defaulting country, and any company or country who has borrowed from its banks is at risk of the same. If Canada has invested in US bonds, and suddenly they're not getting their return, then this entire process happens again in Canada, though on a smaller scale.
So, what to do?
Well, the only thing a country can do is bail out the defaulting country, otherwise it may lose everything it has invested. If I depend on my 300m in bonds coming in, then I may have to spend 1B protecting that investment and hope that the country is back on its feet firmly so that they can keep paying back my investments as well as paying back my bail out.
This is a simplified version and may be a bit inaccurate, but this is basically how it all works. Keep in mind that experts have written books 600 pages long explaining this process and it is extremely complicated.