It means, in effect, benefits to which aliens are entitled: for which the requirement to establish citizen/alien status is waived (that is, applicants are exempted from the requirement to establish it).

"Citizen/alien status" doesn't mean that someone is both a citizen and an alien; it refers to establishing whether you are a citizen or an alien. In effect, it means that it is not necessary to establish that you are a citizen in order to have access to these benefits.

It seems to apply particularly to medical attention:

"Citizen/Alien-Waived Emergent Medical (CAWEM): Emergency Medicaid for aliens who have a life-threatening need for medical help. To be eligible for CAWEM, a person must meet all the eligibility requirements of any medical program except for citizen/alien status."
http://apps.state.or.us/caf/fsm/15ncwg2.htm?newwindow

"Citizen Alien Waived Emergent Medical
Eligibility Requirements. To qualify for CAWEM, a person must meet all the nonfinancial and financial eligibility requirements for another medical assistance program, except the citizen/alien status and Social Security Number requirements. CAWEM applicants who are not documented (do not have a legal immigration status) are not required to declare or provide proof of their citizenship or immigration status."
http://www.dhs.state.or.us/spd/tools/program/cawem.htm

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Note added at 31 mins (2013-09-27 20:17:56 GMT)
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So it is not "alien-waived", but "citizen/alien-waived", which is an elliptical way of say "proof-of-citizen/alien-status-waived".