If a country forcibly leaves the Eurozone, is it possible for banks within this country to maintain existing euro deposits? Or does leaving the eurozone mean those deposits are automatically converted?
Arguably the problem all along with the Eurozone (and any other currency union) is the operational mechanics of the underlying banking system.
From a systems perspective, banking systems statistically multiplex liability bank deposits against asset cash and electronic equivalents. (It is mostly electronic these days.) Broadly speaking, the main function of the asset money is to provide an interchange mechanism between banks, and the deposit money is what is actually used to perform economic transactions.
There is no way of enforcing what physical currency gets used as the interchange mechanism. It doesn't really even need to be a recognised currency, and several precious metals have been used in the past. However, if a banking system uses a physical currency whose quantity is outside of its control - i.e. the money is printed by somebody else, then the banking system will collapse over time, unless there is net flow of the currency into the system.
Now, if we look at the greek money supply figures, and we know that that there are essentially three ways for liability deposits to decrease as shown - loan repayment, loan write-off and cash withdrawals, we can deduce pretty easily that Greece is experiencing a massive outflow of cash. We can assume that some of it is cash withdrawals particularly recently, but some of it also debt repayment to debt owners outside of the Greek banking system. As a very rough rule of thumb, on a 25 year loan, about twice as much money will have to flow back to the lender, as was originally borrowed, and this is what's causing the underlying systemic problems.
According to the Wall Street Journal, this is a summary of the debt picture:
Mechanically speaking then, the only way a country can unilaterally stay in the Eurozone is if they are experiencing a net inflow of asset cash/money, in which case it's unlikely that they'd be under pressure to leave it. What this counter-situation does to the economy depends very much on how the banking system is regulated, and since most countries no longer depend on asset cash/aka reserve regulation as a control, the answer as also seen in the US with TARP is not necessarily very much.
A water analogy may be slightly helpful. As long as there is enough water, and any excess can be stored, then it doesn't matter if over time more water comes in than can be used. However, it's disastrous to not have enough water - and that's essentially the problem that the banking system is currently causing for Greece. The various attempts to "solve" the problem by issuing more debt, simply act to make it worse over time.
there is no treaty provision at present for a Member State to be expelled from the EU or EMU (http://www.ecb.europa.eu/pub/pdf/scplps/ecblwp10.pdf)
Now could such a provision be added?
The first objection to reading a right of expulsion into the treaties is a formal one. A Member State’s expulsion from the EU or EMU would inevitably result in an amendment of the reaties, for which the unanimous consent of all Member States is necessary under Article 48 TEU. Given that a Member State’s expulsion would, by definition, be contrary to the presumed wish of that Member State to continue its membership of the EU, a right of expulsion would be inconceivable, since it would have to entail an unauthorised Treaty amendment, in breach of Article 48 TEU. Besides, it is likely that some Member States would object to the introduction of a right of expulsion in the treaties, coupled with an amendment of Article 48 TEU to make that possible, since this would expose them to the risk of being forced out at some future date.
Moreover, apart from it being politically almost inconceivable, forcing a Member State out of the EU or EMU would inevitably give rise to tremendous legal complexities. ... ‘participation in the European Union gives rise to a wide web of rights and obligations to citizens, companies and governments. To erase all those obligations at a stroke by expelling the member state would create huge confusion and penalise ordinary citizens and ordinary businesses, who rely on their rights of residence and free movement, to name but two’