Does the spouse have any claim to the deceased social security?

What you are referring to is what is commonly called 'survivor's benefits' or 'survivorship benefits'. The spouse, children, and even an ex-spouse could be eligible for these benefits. Every situation is different though and not everyone will qualify or receive these type of benefits.

The best place to find your answer is directly from the Social Security website (http://www.ssa.gov/) or by contacting your area office with the question.