In some European countries, the salaries and pensions of working people have been cut because governments are in debt to control banks and lenders.
不定式可以看作方面状语，意思是“在控制银行和贷款机构方面是负债运行的”。还有一种可能的分析是：介词短语 in debt 修饰不定式作方式状语，即“负债控制”。
跟下句是一样的结构：
Dave was in a hurry to get back to work.
