If I'm drawing my SSI & my husband dies, can I stop drawing my SSI & draw his?

Hi,

Not exactly. If your husband dies and you are eligible for widow's benefits (https://secure.ssa.gov/apps10/poms.nsf/lnx/0300207001), you would continue to receive your own retirement benefit plus an excess widow's benefit, assuming that his benefit rate is higher than yours. And, if you're full retirement age or older when your husband dies, your total benefit rate would equal at least the amount that he was receiving, and possibly even a bit more if he filed for reduced retirement benefits.

I should clarify that my answer assumes that you are currently receiving Social Security retirement benefits, not Supplemental Security Income (SSI) which is a needs based program administered by the Social Security Administration.

Best, Jerry