Sequence of tenses missing - not in Reported Speech

Simply because He was believed to have been in debt would refer to a time before the time when the thinking was going on: they believed (a year ago) that he had been (two years ago) in debt. (This is sometimes called the pluperfect, to distinguish it from the normal past tense.) Strictly speaking, there is no implication one way or the other whether he had paid off the debt in the meantime; but if he had not, it would be both simpler and more informative to use the normal past.

Even more simply: Consider your first sentence: you did not say they believed he had been in debt.

'to be in debt' means that he hasn't come out of debt.

'to have been in debt' means that he has come out of debt.