What is the ruling on the state obliging an indebted expatriate to pay Zakat despite his need and his compulsion to take out a loan to pay it?

If the Imam requests Zakat, it is obligatory to pay it to him, even if there is a dispute regarding its obligation due to debt or other reasons, because the Imam resolves disputes through his ijtihad (independent reasoning). And if you are a debtor, you are eligible for Zakat, and it is permissible for it to be given to you.