Having a credit card entitles the owner to conveniently purchase products and avail of services without having to pay in cash. But it also entails responsibility on the part of the owner to pay whatever amount he has expended using such credit card, as well as the penalties, interests and/or surcharges which he may have incurred.
Considering that your mother has already passed away, her estate shall be made liable for all her debts and other outstanding obligations. However, her heirs will be held liable to pay for her obligations if she has left no property, whether real or personal, to answer for the same. This is in line with Article 776 of the New Civil Code of the Philippines which states that inheritance of the heirs includes all the property, rights and obligations of a person which are not extinguished by death. In addition thereto, Article 781, id, provides that the inheritance of a person includes not only the property and the transmissible rights and obligations existing at the time of his death, but also those which have accrued thereto since the opening of the succession. (emphasis supplied)
Consequently, it is advisable for her heirs to inform the bank regarding the demise of your mother so that the bank can terminate your mother's contract with them insofar as her credit card is concerned and in order for the proper officers of the bank to send the heirs a copy of your mother-in-law’s billing statement. If you are the only heir left by your mother, it would be best for you to coordinate immediately with the bank and inquire whether or not your mother has pending obligations with them. If your mother has outstanding debt, it is important to settle the same before its due date so that your mother's estate or her heir/s will not incur any penalty or surcharges.