What kind of 政府廉租房 (English name) are you talking about? Is it nursing home, senior housing or low income housing? Do you live there for long term?
Here is the USCIS website about the Public Charge and it clearly state what kind of benefits not subject to Public charge consideration, but is not specific for what kind of benefits will subject to public charge. So, you may consult a lawyer for this issue if you live the 政府廉租房 for a long term.