What is the opposite of public debt?

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).

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.