You could consider filing in Surrogate's Court to be the administrator of her estate. You may quality to file as a small estate which is less complex and less expensive in terms of fees , As administrator you can notify the creditors and the landlord of her death and lack of assets You can then make arrangements in regards to the apartment The creditors will be limited to taking a share of whatever is in the estate and writing off the remainder If there were only a small number of creditors you might be able to provide notice to each of them simply with a copy of the death certificate, With a mountain of debt you may want to send notices concerning the filing in Surrogates court. The creditors have rights to make you prove the lack of assets but once you have done so they can not get money that isn't there Good luck and talk to a lawyer for detailed advice
If the estate net worth is as negative as you state then you are better off doing nothing.....you have no legal duty to start an estate proceeding as there will be no assets left for family members and worse....you would in fact be exposing yourself to liabilities if you were to assume the mantle of executor. My suggestion is to do nothing and let the creditors hash over whatever is left for them to haggle over...let them file with the court and do all the legal stuff...you can simply not get involved.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained. Please click "helpful" or "best answer" if my answer added any value or add a "comment" if you have more info for me to help you get a better answer.
I lean towards the opinion of Mr. Corrigan.
I may be guessing or not licensed in your state. No atty/client relationship exists.