First, I want to second June's suggestion to do all your testing on a test copy of your data. Back up your database early and often, and do your fumbling in a junk copy.
Second, I wanted to point out that social security numbers are not unique. Two people can have the same one. It's not common, but it can happen, because the first five digits encode meaningful information, and they reuse the numbers after people die (and sometimes before).
As such, you should use your date of death (or month and year of death) as an additional qualification on your update. the SQl for that should look something like this:
Code:
UPDATE tblNewDeceased AS TNew, tblAllDeceased AS TAll
SET TNew.MyAlias = TAll.MyAlias
WHERE TNew.MySocial = TAll.MySocial
AND Month(TNew.MyDeathDate) = Month(TAll.MyDeathDate)
AND Year(TNew.MyDeathDate) = Year(TAll.MyDeathDate);
Obviously, you'll need to substitute your field names and table names, or do it in the query designer.