A:
Committing suicide is Haram (prohibited) for which there is severe punishment. However, this does not take the person out of the fold of Islam, for it is a major sin other than Shirk (associating others with Allah in His Divinity or worship). One who commits suicide is still regarded a Muslim and so it is permissible to supplicate Allah for them, give Sadaqah and offer Hajj on their behalf. All these are acts of obedience that will avail them if Allah accepts them.
As for the debts due on the woman who killed herself, they should be repaid from her estate. The objects she left are to be sold and the debts are to be repaid out of its total value. Her children are not entitled to any share of her estate except after her debts are paid in full. If there are still some debts that have not been paid, they are still due on the deceased and it is not obligatory on the children or the husband to pay her debt, except by way of charity. They and other Muslims should seek Allah's Reward and participate in the payment (Part No. 7; Page No. 217) of the remaining dues.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.