In new york state if I was to die and carried unsecured credit card debt would my wife be responsible to pay?

my father has about 40,000 in unsecured credit card debt, the cards are in his name only with no co-signer. he has terminal stomach cancer and is now going to hospice care, he is very worried about this debt. in new york state when he pes away is my mother going to be responsible to pay these cards off? she is on a fixed income with not much ets or resources?? any help would be greatly appreciated