Is it obligatory to pay the wages of a housemaid who ran away before completing her contract and has not claimed them, given that her mother is the one claiming them, and the amount does not cover the losses?

Contracts are the law between the contracting parties. If you agreed with the maid on a specific work duration, she is not allowed to annul the work and abscond without your consent. As for the salary, if she leaves the work before the agreed-upon period ends, a portion of her salary commensurate with the duration she left can be deducted. The predominant view is that she is entitled to the wages for the work she has performed. As for recruitment costs and similar expenses, this refers back to the terms of the contract or the prevailing custom in the country.