Is it permissible for a wife to perform Hajj or 'Umrah if her husband is deeply in debt?

A wife is not obligated, according to Sharia (definition), to pay her husband's debts, except as an act of charity and solace. She is required to perform the obligatory Hajj and Umrah (definition) if the conditions are met, even if her husband is in debt.

As for voluntary Hajj and Umrah, they are intrinsically better than voluntary charity. However, if the husband is in debt and in need, helping him repay his debt may be better. The matter requires elaboration, and preference is given to what fulfills a greater need and provides a more comprehensive benefit.