To answer OP's question fully, in MX IRROPS, DL will provide a voucher for a hotel.

Occasionally, DL will reimburse up to what it would have paid, but that is rare and takes a lot of time and effort. Also, to be clear, air carriers contract for bulk rooms at airport hotels (largely because most hotels can't sell rooms after 10 PM) and pay extremely small amounts for those vouchers. The reimbursement, if you were to be able to get it, would generally be very small.