Singular "debt" should also be accepted, I think - I would usually talk about "being in debt" or "having debt", in the singular, regardless of how many people I owe money to.
So at least "The professor does not have any debt" + "The professor is not in debt".
@a1.el.en.1 (mizinamo?) I can't speak for AE but certainly in BE we refer to someone as being "in debt" in the singular and "having debts" in the plural, irrespective of whether or not the debt/debts themselves are singular or plural. We do not normally refer to someone as "having debt", if we want to emphasise the fact that the debt is singular we say that they "have a debt outstanding" or, " have an outstanding debt". I hope this is useful.
When hovering over the word "καθηγητής" you get the translation "professor" and "teacher". So I don't get why DL would not accept "the teacher has no debts" as a valid translation for this. PS: I know the difference between a teacher and a professor, both in EN and GR.