There is no such thing as "maaser-free income" — we owe maaser on ordinary income, interest, and gifts — even on tax-free interest. Even a poor person who survives on donated tzedaka — in other words, all of whose income comes from money that itself has been given as maaser — is required to give maaser on the tzedaka he receives.
With regard to your unemployment insurance, there are different kinds, some of which are taxable and some of which are not. I am very much inclined to say dina d'malchuta dina — we follow the law of the land — and thus if your unemployment insurance is taxable income then it is subject to maaser.
Having said that, there are several potential leniencies available to you.
Now, since I noramlly calculate annually, if chas v'shalom I am unemployed do I immediately need to tithe my unemployment insurance on receipt? No — I can wait until the year end with the hope that before then I will have a job with greater income again. Thus I accumulate a maaser defecit that I owe and will make up before my calculation period closes.
But if I normally calculate monthly, weekly, or daily, then it would much more of a leniency to move to an annual calculation just for the purpose of delaying my maaser obligation. I would be stricter with regard to such a change of my established practice.
I hereby separate this money for maaser. Should I — G-d forbid! — become impoverished such that I need this money, I will be eligible to receive this maaser as a loan to myself which I will repay when Hashem provides me with the means to do so. After repaying the loan, the money repaid will either be kept in a loan fund for others I encounter in such a situation or will be given away to an appropriate charity. Should I — please G-d! — return to work without ever needing this money, I will then give this money to an appropriate charity. May it be Your Will, Hashem, that by the merit of my separating this maaser, I soon find an appropriate means of supporting myself.There is no need to actually verbally declare this, though doing so will both make it a firm commitment that you will have to keep according to Torah Law and make it a personal prayer. You may want to add a Psalm or two if you decide to go that route.
I hope this is helpful. It is clear from your correspondance with me that you take maaser seriously, and that itself is of tremendous spiritual merit for you. May Hashem soon reestablish your means of supporting yourself.
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