When the Central Bank sells a bond, where does the money go ultimately? As the accepted answer points out, the premise of my question was flawed. Thank you for the dispelling of my wrong assumptions. The original question follows.

There are two related questions (and feel free to assume the Central Bank in the questions is USA's Fed):


When the Central Bank sells bonds, where does the money go ultimately?
How separate is the Central Bank budget from the government's budget?


To clarify: If the Central Bank sells \$1000M worth of bonds in order to repay \$800M old maturing debt and to raise an extra \$200M, does this \$200M simply become available for use to the government? Or is there some extra process in order to transfer money between the government and the central bank? Who decides (central bank, executive branch, legislative branch) how much new debt the central bank will be selling?
Firstly, the central bank doesn't issue bonds. The treasury (in the executive government) does, as a way to finance government expenditure, and make real investments in the economy.

In modern economies, the central bank's primary focus is the interest rate at which they lend money to private banks. If they require more money in order to finance those loans, they will simply create more money, as they have the legitimacy to do that. (Note that most money that is created is not physically printed, but rather it is just the electronic entry of that currency, in the initial transaction. An economy requires a fraction of electronic money to exist as cash, so a fraction of created money is printed.) However, fiat money requires some security to give it legitimacy. To this end, the central bank holds securities, stocks, precious metals, cash and foreign currency in its reserves. You can see here that bonds form part of those reserves, so that is why central banks buy treasury bonds. Plenty of other domestic and foreign financial institutions also buy treasury bonds, as part of their reserves to give legitimacy to their "demand deposits" (which is fiat money), or as part of a strategy to lower the risk of their investment portfolios. Private banks also create money by loaning out their demand deposits.

Analogously, if the central bank raises the interest rate (in order to curb inflation), they will be slowing down the growth of money (which can be thought of as a "leakage"), and that is a situation in which they would buy fewer bonds.

Central banks need to operate autonomously from the executive government, and this autonomy is usually enshrined in the respective country's constitution. When this doesn't happen, the executive government could force the central bank to buy their bonds, which creates a huge injection of money into the economy. This money that is created belongs to the government, so they spend it in order to achieve policy goals, however, after a while the currency becomes worth less and less (as inflation is high). That is the main cause of high inflation. When the central bank is autonomous, they have control over the monetary system, and keep inflation in check with the central bank interest rate.