In what case is stealing permissible in Judaism? For example, is it a sin for a Jew to steal in case he doesn't have an income or a job? (and of course it is hard or impossible to find an alternative)
I disagree with the example suggested, in a case where the person doesn't have an income or a job.
There is a Talmudic principle, that (generally speaking) laws of the Torah can only be abrogated in the case of "Pikuch Nefesh", when there is immediate danger to a person's life.
Therefore I don't see how stealing would be permitted if a person is broke, and has no job. Since he can always try begging, by which he would get money in a legitimate manner, then the Pikuach Nefesh dispensation is inapplicable. The fact that he may be embarrassed to beg, doesn't give him license to steal.
A scenario where stealing would be permitted, is when a person's life is in danger, and by stealing he would alleviate that danger to his life.