I assume that you are asking about the two times in late 1995 and early 1996 in which the federal government was “shut down” because of disputes between President Bill Clinton and Republicans in Congress over the budget. The government did not exactly run out of money. Instead, it could not agree on how to budget the money and therefore it no longer had legal authority to spend.
In late 1995, the Republican leadership in Congress wanted to reduce government spending. However, this did not fit with President Clinton’s desires. Congress passed budgets that reduced spending, but Clinton vetoed them. This meant that there was no legal authority for the government to keep spending. Therefore, the government shut down functions that were designated as non-vital for a total of 28 days. The shutdown continued until the two sides could agree on a budget.