As long as a person is permanent residence,he or she is eligible for food stamp and Medicaid. This type of program is only offered for people with low income ,so they should qualify for it.
 I have seen one family who came over here after winning DV lottery and were eligible for medicaid and food stamp. I don't think it will be problem. One thing they need to do is apply for social security card immediately.

Eligibility and Issuance Requirements for food stamp(california)

http://www.dss.cahwnet.gov/foodstamps/PG841.htm#citizen