Not unless her next of kin was her husband, if this was the case, then yes he would be liable for the remainder of the loan. It is likely the loan company asked for next of kin, as a means of contact in the event of her death. Otherwise, if she is single, it is likely they would ask for a guarantor. Deciding to be guarantor for someone is not an easy decision, as in the event of default on the loan, or death, then the guarantor would also be liable for clearing loan.
Hope this helps.