If someone can't finish the month financially, and has to borrow or take gifts in order to feed his family, does he still have to give Maaser from his salary?
Talk to your rabbi.
We rule that tithing of funds is a very meritorious practice, but not an all-out obligation. The Talmud prohibits one to give too much, lest they impoverish themselves and become a recipient.
As I'd heard in a speech on maaser kesafim from Rabbi Yitzchak Breitowitz (and see the late Cyril Domb's book), feeding one's family comes first. Consult your rabbi if part, or all, of your tithing funds should go back to your own home.
Shulchan Aruch does discuss giving a token sum per year, to show that we belong to a people that believe in kindness, but that's not very much.
First of all, the Biblical mitzvah of maaser has to do with produce; the contemporary version of the mitzvah, maaser kesafim, where one gives 10% of his income, is a minhag or at least of Rabbinic origin, according to most poskim.
The Gemara, at Kesubos 50a, states that one cannot give double-maaser (20% of one's income) if it would cause him to be impoverished, however, there are exceptions to this rule.
There is a split among the sources whether a poor person must give maaser. Some rule strictly and require maaser even of the poor unless they can't even purchase bread and water, others take the position that if one has to rely upon others to satisfy basic needs, and has no luxuries, then he need not give maaser. See Teshuvos V’Hanhagos 1:560, Kuntros Kol Torah Choberes 39 B’Shem R’ Shlomo Zalmen Aurbauch Zt”l.
However, the Gemara is quite clear that the poor should nevertheless give tzedakah (which is a separate mitzvah from maaser). At Gittin 7a-b, Rabbi Avira, interpreting Nachum 1:12 which states: "If they are complete, or many, even so they will be cut" - states: "if one sees that his income is scarce, he should give Tzedakah from it, and all the more so, if his income is large!" The Gemara cites its agreement stating: "If one trims his possessions and gives Tzedakah, he is saved from punishment in Gehinom." Continuing the reading of Nachum 1:12, "And I afflicted you," Mar Zutra finds that proof for the point that "even a poor person supported by Tzedakah should give Tzedakah." And from Nachum 1:13, where G-d continues and says "I will not afflict you any more," Rav Yosef finds this to be a proof that the poor will be rewarded for giving charity because he will cease being poor.
Bottom line, if one thinks he might be poor enough to be exempt from maaser, he should consult his local rabbi.
It is possible to give too much. The gemara, at Ketuvos 50a, says that one should not give more than a fifth of their income (double maaser) lest he comes to be a charity case himself.