Here is some info I quote from the MSN site. Somebody asked the similar question. Below is the reply from one member.
Some info from murthy.com
Chat User : I am in the process of changing status. Can I apply for unemployment benefits? Will I get in trouble later when I apply H-1 or PR if I try to apply for unemployment compensation?
Attorney Murthy : Yes, a non-immigrant may have a problem in taking unemployment since that could prevent the INS from allowing him/her to be considered not a financial liability on the U.S. After getting the GC, it is not a problem if applying for citizenship.
Chat User : Would it be prudent to apply for unemployment upon being laid off while still having a valid EAD and awaiting I-485 adjudication?
Attorney Murthy : Individuals who are likely to become a "public charge" are not eligible to adjust to status to permanent residence. Unemployment is generally paid for by the employer, as mandatory insurance, and not the government. However, there may be instances where it is not 100% employer supported. Therefore, although it is not absolutely clear that it will cause a problem, or even come to the attention of INS, it is also not 100% clearly safe. In general, it is best to avoid any such issues, unless there is simply no other choice. Eligibility for unemployment compensation is a matter of state law, so it is different state to state.
Chat User : Hello Ms Murthy, I have an Adjustment application pending with VSC. Will taking unemployment benefits (unemployment insurance) after a layoff, have a negative effect on my application?
Attorney Murthy : If the insurance is from a gov't-sponsored program then it could be a problem to obtain permanent residency. If it is private insurance with no gov't funding then it may be okay. Most gov't sponsored funds taken by an applicant for GC, could create problems in obtaining the GC, though all money paid into the system will be helpful after you become a GC holder to help you and your family members if certain conditions are fulfilled.
Chat User : 180 days have passed after I-485 filing. My wife, the beneficiary in the filing, got laid off recently. Is it safe for her to claim her unemployment benefit without effecting / jeopardizing her AOS? Thank you very much!
Attorney Murthy : Many scholars believe that certain types of benefits are employer paid and not a government benefit or subsidy, so should not be counted against the foreign national in denying the I-485 application. Others believe it is safest not to take any form of benefit since it reinforces the notion that the immigrant should not become a "public charge" but should be financially independent in the U.S. Also, it may be helpful to consult a benefits attorney who is more knowledgeable on some of these issues since eligibility for benefits and the impact on the immigration processing may depend on various factors.