Question: The opposite of a budget deficit is a budget surplus

But what is the opposite of public debt?

Instead of govt/state being in debt, having the government have extra money to keep or to lend it to banks or companies.

Say the extra money are kept Instead of being lent. What is the name of such a surplus?
It would be the sum of the budget surplus for the curent year and all the years before.

Answer: 
Such government would be called net lender. However, note that for a country to be net lender it is not required that debt is zero, only that the amount it is lending is higher than its liabilities (debt). A country can chose to have some level of debt even if it is not necessary for it to have it because its revenues are higher than expenses. An example of net lender would be Norway (see [here)](https://www.oecd-ilibrary.org/economics/national-accounts-at-a-glance-2014_na_glance-2014-en).
The opposite of liabiliteis, i.e. debt and own equity, is assets. The net of outstanding financial assets and liabilities is by definition zero as one party's financial asset is by definition the counterparty's debt. The net of libilities and assets in a balance sheet is also by definition zero. A government can keep assets for instance in a sovereign wealth fund. One could here mention Norway which has collected oil revenue in a govenment owned wealth fund and which by the same time runs a very small public debt.

The opposite of public debt would be public assets in so far we don't expect it to be any equity in the public balances.