It says in chapter 254 of the Shulchan aruch that if you really need Tzedaka and what you recieve from “israel” is insufficient,then you may ask from goyim. The Shulchan Aruch continues to explain that when turning to goyim for donations you should do so privatly. Finally, if you are unable to collect in the prescribed manner,you may do so publicly. Since the obvious concern here is blasphamy of G-d’s name, to what extent or degree of poverty must one arrive at in order to sanction such an act? Secondly, are there any limitations on what you may use the “goyish” money for and how do donations from such anonymous jewish sources differ. We are in so much debt that we risk being evicted from our apartment and we can’t keep up with the grocery bill not to mention paying tuition for 4 (four) childern in school. We want to abide by the very words of Halacha,yet we don’t know what price we can afford, so to speak. We appreciate your assitance and may Hashem bless you and all of us and help us learn, listen and perform the entire torah in prosperity and good health.
The circumstances you describe (inability to pay the grocery store and tuition for the children) is sufficient to permit receiving charity from non-Jews, if necessary, even publicly. However, effort should be made to ensure that the charity should be received in a discreet way.
Although the Gemara in Bava Basra (10b) writes that it is forbidden to receive money from non-Jews, the Gemara in Sanhedrin (26b) writes that the prohibition applies only to donations given publicly, but not to donations that are given privately, and for which the issues of chilul Hashem is not raised. This distinction is ruled by Rambam (Matnos Aniim 8:9) and Shulchan Aruch (Yoreh De’ah 254:1-2).
However, Rambam and Shulchan Aruch also mention the rationale used by the Gemara in Bava Basra, namely, that accepting charity from non-Jews gives them “credit” that we do not wish them to have. This rationale would seemingly apply even to private donations, a problem for which several authorities suggest answers. Derishah (YD 254) writes that the Gemara only forbids accepting charity from non-Jews when the charity is given to a charity collector (gabbai tzedakah), and not when the poor person himself receives the donation. This answer is also found in Orchos Chaim (vol. 3, 34:1), and is implied by Meiri (Bava Basra 10a). Taz (254:1), however, disputes the solution, suggesting instead that the prohibition applies specifically when the non-Jew desires the special merit of contributing to Jews. A similar approach is taken by Binyan Zion (85). According to Maaseh Roke’ach, the prohibition applies only to a large amount that can be shared among many poor people, and according to Shenos Chaim (181d) the prohibition applies only to kings and officers, an opinion also voiced by Rav Elyashiv (Moriah, Adar 5747).
According to all of the authorities mentioned above, no prohibition would not apply to cases of private donations (see further a previous post, where we have elaborated further on the subject). Under normal circumstances, it would be possible to arrange for the money to be given in a relatively private forum, without giving publicity to the specific donation, and to the fact the receiver is Jewish.
In addition, as the question notes, when Jewish donations are not sufficient, and money is required for basic living, it is permitted to request charity even in public.