Q: Someone is struggling to pay off her debt, can I help her with my Zakat?
A: Yes you can help her if she is eligible to receive Zakat in the first place see link.
The other school of jurisprudence i.e. the Malikis, Shafi'is and Hanbalis have also added a condition; that the nature of the debt must Islamically lawful.
Hence according to them, if the debt was incurred due to a sinful reason such as gambling, then giving Zakat to such person would not be permissible unless they have repented from this sin in which case the Zakat can be given to them.