I'm not sure this is an "idiom", but certainly associated with the bookkeeping.
For example, if a company purchase, to say, a 10 million dollar building by borrowing from a bank, the accountant makes an entry into the journal such as
below. ( And the company can not pay the debt worth 10 million at once but by
Building 10,000,000 USD / Long term liability 10,000,000 USD
The left side, in the bookkeeping worlds, almost always records asset type items, such as money in the bank, cars, long term investment ( such as 10 years-maturity bond ), and so on. ( but not necessarily ), and the right side records the debt type, or capital, and accumulated incomes ( which is, incomes accumulated so far. )
Trump says Putin's support is an asset, not a liability.
means Trump is saying Putin's support is equal to money to help him not a burden aka debt to him.