Yes, a person who owns a home and lives in that home can be eligible for SSI benefits. For more information, read the Social Security Administration’s booklet, Supplemental Security Income (Social Security Administration Pub. No. 05-11000).
A "home equity line of credit" is a line of credit allowing the borrower to draw down loans from time, secured by the borrower's home. Home equity loans allow a borrower to potentially borrow large sums at an attractive rate.