The answer to this question is yes and no. There are two types of Social Security Disability, and permanent residents that have not paid taxes can receive one form of disability: SSI. SSI (Supplemental Security Income) does not require anyone to pay taxes to receive benefits. You must simply qualify medically and financially.
On the other hand, the DIB (disability insurance benefits) can only be received as a result of paying into Social Security through taxes. If you have not paid taxes, you may not receive DIB; it's as simple as that. Read more about the difference between SSI and SSDI.
Because the rules are so rigid and complex, it may be a good idea to talk with a Social Security attorney to see if you qualify.