With the possibility of Greek exit from the euro zone drawing closer, it's becoming a little bit clearer what Grexit could really mean for Greeks and their economy. And the prospects aren't very pretty.

The biggest problem now is that Greece's banks are rapidly running out of cash. The banks have been closed for a week; ATM withdrawals are limited to just 60 euros (about $66) a day and could fall further. Without access to cash, many Greeks are unable to pay their bills or buy food, medicine and other daily essentials.

Greece is now desperately trying to craft a new proposal for a bailout plan; on Thursday, it was finalizing details of the request. It's still possible that the euro zone will reach a compromise to rescue Greek banks and allow Greece to stay in the euro zone.

That would still be the best scenario for the Greek economy, says Jacob Funk Kirkegaard, a senior fellow at the Peterson Institute for International Economics.

But if that doesn't happen, Greece has two options to finance its struggling banks, Kirkegaard says. One is to recapitalize its banks by giving its depositors "a haircut" — basically taking over some of their deposits. In 2013, Cyprus forced bank depositors to give up about half of their deposits above 100,000 euros that were held in local banks -- a so-called "bail in."

The other option, says Kirkegaard, is to abandon the euro altogether and attempt to restart its economy with a "new" currency — probably the drachma, the currency Greece used before it joined the euro.

Some see the drachma as the solution to Greece's problems. If Greece had its own currency, it could print more money, which would lower the value of its currency and make its products cheaper. That would make exports, Greek vacations and investments all seem more attractive to foreigners, helping to jumpstart the Greek economy, and boosting employment.

But there are a lot of problems with that scenario, says Kirkegaard.

The first issue is just the logistical nightmare of switching to the new currency — printing enough cash to meet demand and distributing it to banks and ATMS. That could take weeks, during which time Greece's economy would be essentially frozen. The result could be chaos.

One way that Greece might bridge this gap would be by issuing temporary IOUs, or "scrips." The government could issue these IOUs as a form of payment for government workers and pensioners, and agree to accept IOUs in the future instead of taxes. But this would be only a short-term solution to the cash crunch, at best.

Even if the logistical challenges are met, there's a more difficult, longer-term issue, says Kirkegaard: Getting people to actually use the drachma, instead of just relying on the euro in their daily interactions.

The (too) mighty dollar

To understand why this might be a problem, look to the experience of the many countries that have switched from using their own currency to the U.S. dollar, and then tried to switch back to their own currency.

Some compare Greece switching to the drachma to Russia or the Czech Republic adopting a new currency after the fall of Communism — which they did successfully. But Kirkegaard says this is a false comparison. These countries phased out the old currency as they introduced a new one, whereas even if Greece introduces the drachma the euro will continue to be one of the world's most important currencies.

The better comparison is countries that have attempted to re-establish their own currency after using a major international currency, like the dollar or the euro. Many countries, especially developing ones, have temporarily given up their own currencies in the past and adopted a foreign currency like the dollar or euro instead -- usually because they are experiencing inflation or some other kind of economic disturbance.

When inflation is rampant in a country, the day-to-day changes in the prices of goods can make it difficult to carry out normal business, and can quickly erode people's savings. So people may start using a more stable foreign currency like the dollar or euro to store their wealth instead.

This process is known as "dollarization," and it can be either official government policy or happen without the government's consent. A country is usually considered "dollarized" when around a third of its monetary supply is a foreign currency, though this can be hard to measure, says Michael Albert, an adjunct professor at the Josef Korbel School of International Studies at the University of Denver.

There are some benefits to dollarization. The main one is that it usually ends inflation right away. But officially adopting a foreign currency can also help convince foreign investors that the country is a safe place to invest again. It can also help a country avoid speculative attacks on the value of its currency, which lead to sudden outflows of capital.

But there are also some significant disadvantages to using another country's currency. The main one is that the country surrenders control of its monetary policy — it can't print more money to finance its own spending, or make the value of its goods or worker wages cheaper. A dollarized country also gives up what's called seignorage, which is the profit that a government makes by issuing money -- the difference between the value of a dollar or coin and its production costs.

Another issue is that its central bank can no longer be a "lender of last resort," providing enough funds to cover losses if there is a run on the bank.

Some of these concerns might sound familiar -- they are actually the primary issues that Greece faces in using the euro. As Greece is now, dollarized countries that can't print money or act as their own lender of last resort are vulnerable to crises of both liquidity and solvency.

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The other issue with dollarization is that it can be very hard to reverse. If a country wants to switch back to its own national currency -- say it wants control over its monetary policy, or simply wants its own currency for reasons of national price -- it first has to convince its people that the currency is more stable and useful than the dollar or euro.

Some countries have succeeded in "de-dollarizing" — Peru, Israel and Poland, among them — but there are more examples of failure than success. Many countries in Africa, Latin America and Asia have been working for years to reduce their dependence on the dollar, though the policy isn't popular with big businesses. Cambodia has been trying to de-dollarize its economy for more than a decade, but in 2010, the dollar was used in nearly 90 percent of transactions.

Even the success stories in de-dollarization come with trials and costs. When Mexico forcefully converted its dollar deposits into pesos in 1982, people sent so much money out of the country that private sector bank credit almost halved in two years. Mexico successfully de-dollarized, but its economy also slowed to a crawl and inflation shot up.

Both Peru and Bolivia also tried and painfully failed to de-dollarize before getting it right. Both countries dollarized in the 1980s after going through periods of devastating hyperinflation. In the 1980s, the countries separately tried to force de-dollarization by converting foreign currency deposits in banks into the local currency. This terrified depositors, who pulled their money out of banks and sent large amounts of their money overseas, shaking the banking system.

Eventually both countries had to switch back to the dollar. It wasn't until the 2000s, after years of stable governance and low inflation, that the dollar's prominence gradually declined in these countries. But even though these countries are "success" cases, the dollar still plays a huge role in their economies -- accounting for about half of all deposits in 2010.

Countries can de-dollarize in two ways: basically, the stick or the carrot. They can either forcefully convert bank deposits to the local currency, or they can try to induce their people to gradually switch over by offering an attractive, stable currency, says Albert.

The international community dislikes the first option for two reasons: It's coercive, and they think it doesn't work. It undermines people's confidence in the currency, and the minute restrictions are lifted, most people will switch back to the dollar or euro, Albert says.

The way that the IMF recommends de-dollarizing is creating a stable macroeconomy -- basically, limiting inflation, or at least temporarily convincing people that they are up to the task. When inflation occurs in a currency, people who are holding that currency see the value of their money fall. Once people get a whiff of inflation, they are much more likely to shift their holdings to a stable currency like the dollar or the euro instead.

So in order to make such a transition, countries need to have very low inflation -- usually created through austerity. The government also needs a lot of credibility -- people need to believe the government can control inflation.

Greece has a problem on both fronts. Austerity is the reason that Greece wants to leave the euro in the first place — it needs its own currency so it can print money and restart its economy. And while the Syriza party may have captured the political inclinations of the Greeks, many Greeks have doubts about their ability to manage the country's finances. Given the current climate, it's not hard to see why Greeks might shift their savings into euros and try to send them abroad.

If Greece switches back to the drachma, it would probably try to convince its citizens that using the currency is a patriotic issue. But it will be hard to get people to be more concerned about patriotism than the value of their savings.