What is required of the one who possesses wealth that is subject to zakaah is to pay zakaah on it when one year has passed since he acquired it, even if he owes a debt, according to the more correct of the two scholarly opinions. Debt should not be deducted from the total amount of wealth on which he is paying zakaah, and it makes no difference whether the time paying the debt is deferred or it is due at present. Please see the answer the questions 22426 and 106434.
Once it is established that debt does not mean that zakaah is waived, then there is no difference between a debt that is owed to Allah, may He be exalted, such as zakaah, expiation and vows, and debts that are owed to other people.
It says in Mughni al-Muhtaaj (2/125): Debt does not mean that [zakaah] is waived, whether it is presently due or not, whether it is of the same type of wealth or not, or whether it is due to Allah, such as zakaah, expiation and vows, or not, according to the most correct opinion and because of the general meaning of the evidence for zakaah being obligatory. End quote.
And Allah knows best.