With RSUs, you are taxed when the shares are delivered, which is almost always at vesting. Your taxable income is the market value of the shares at vesting. You have compensation income subject to federal and employment tax (Social Security and Medicare) and any state and local tax.
If you're sure Social Security tax was not withheld from your husband's RSU compensation in 2016, I would suggest you contact the payroll department at his ex-employer and request a corrected W-2. If a corrected W-2 is provided, you can then file an amended 2016 return.
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