What effect would destroying large amounts of physical currency have on government finances India has recently recalled high denomination notes and asked people to deposit the physical currency in old notes in their bank accounts. People who have unaccounted wealth are resorting to destroying the currency rather than run the risk of declaring this to the tax-men. Some people estimate upto 20% of notes may not be returned totalling about  3 trillion rupees.

In a cash based economy what possible consequences can destruction of such large amounts of currency cause? I think that reduction in money volume may lead to negative inflation but the question is more about the impact destruction of currency will have on government finances.
Does it make the government richer or poorer? 

Note that this question isn't about demonitization per se.

EDIT:

A newspaper report this morning says that the government expects a "windfall" due to cash not being returned by people. It states that any money not returned to central bank (In India that is the RBI), is a reduction in liability of RBI and therefore an equal amount can be paid by RBI to the government.

Is this how monetary policy works?

I was always under the impression that central bank buys government bonds in return for currency. Any physical reduction in currency means government cannot buy the same bonds back from central bank (as it doesn't have the hard cash) and therefore the government should become "poorer" (due to inability to decrease its debt in forms of bonds issued to central bank). The report states that government will get "richer" as central bank's liability is decreased and it can pay that amount to government as dividend.
Can someone clarify how this process is likely to work?
In most modern economies, the central bank certainly has the authority to print money, when it does so to implement its legally defined objective. Let's consider what the implications of this 'elimination' of cash are.

The Balance Sheet

From the asset management side of the central bank, currencies are always a liability - because, amongst other things, they can be deposited in an account with the central bank, which will usually accumulate interest payments. Historically, many central banks used to allow currency to be exchanged for gold.

Central banks must always be concerned with their balance sheet. The reason why they cannot simply issue and distribute it to the masses (known as helicopter money) comes down to this management of liabilities - there is a real constraint here for these institutions. Issue too much currency, and commercial banks might not think you will be able to pay interest on their deposits. Or more aptly, they may believe the only way you can pay this interest is by printing money, decreasing the value of money and  potentially leading to inflation or a runaway zimbabwe situation

So the destruction of currency reduces the financial liabilities of a central bank, benefitting its balance sheet.

Impact on the Economy

Now we can look at the implications for the economy. Shown below is the fisher equation, a simple but valuable representation for money interacts with the economy.

$MV = PY$

This indicates that real output (the right hand side) is equal to the amount of currency in circulation, multiplied by how quickly that currency is circulated around. So if a central bank wanted to keep prices and output constant, it would want to eliminate any changes to the money supply. Otherwise, as you have intuited, there may be a decrease in output or the price level.

But we have to consider if this is really currency in circulation. Are people really using these large denomination notes in actual transactions, or just as a store of wealth? If this currency was unused to begin with then maybe there won't be much of a real impact.

We must also consider that central bank's typically interact with commercial banks only, and are typically most immediately concerned with maintaining their target interest rate with those commercial banks.

How might this play out in practice?

First, these protesters having burned some of their money and so may replace it by withdrawal from their accounts with commercial banks. These commercial banks distribute this physical currency out to consumers, and have less remaining to loan to between themselves. Since for them, loanable funds are more scarce, there will be upward pressure on interest rates.

To maintain the target interest rate, we will then see the central bank response, purchasing bonds from the commercial banks in exchange for cash. Thus the balance of money is restored.

But perhaps this destruction of money was great enough that it has made consumers considerably poorer. Now their bank balance is reduced, they may not want to spend as much. Over the short term, this would be expected to drive down prices and output.

If the central bank sees this play out, or is worried enough to anticipate it, it would likely reduce its interest rate target. With a lower cost to borrowing, we have increased spending in the economy, inflation of asset prices that make people feel richer and hopefully, a restoration of balance.

This is a hypothetical, and relatively simple policy analysis. A less conventional central bank could throw replacement money out of a helicopter, but this seems unlikely to happen in practice.

How does this effect the government?

It will likely benefit them. As I discussed, currency is a liability for central banks. So now some of it is gone, they can print more without having to demand any kind of asset in return. The article you have edited into your question argues that the central bank may print and give money to the government. Normally, because money is a liability, they would have to demand government debt in return. But because the balance sheet already incorporates this currency (which is just replacing what has been destroyed) it need not demand government bonds --- so the government can spend without incurring any debt.