Was she ever married? I'm not certain, but I think she could qualify for spousal benefits regardless of how many credits she has herself.
She should qualify if her spouse died while they were married or if she was married for at least 10 years before divorcing and never remarried.
Yes, married 40+ years and her DH elected the 50%. Would her benefit increase if she got to 40 credits?
In typical circumstances, she'll get the greater of half of her husband's benefit or her own benefit. She won't get both.
So if she's getting $1,000 a month based on her husband's record, she can do nothing and continue to get that. Or she can go through the hassle of getting the additional 12 credits. Then if her own earnings record with the additional 12 credits of earnings shows she's entitled to $800 a month on her own record, she would get the greater of $1,000 or $800, which would mean she would get $1,000. In other words, she would get no increased benefit.
If her own earnings record with the additional 12 credits of earnings shows she's entitled to $1,100 a month, she would get the greater of $1,000 or $1,100, which would mean she would get $1,100. In other words, she would only get a modest increase.
If you learn the formulas, you could do some rough calculations to figure out how much her own benefit would be if she were to get the full 40 credits.
Also note that in order to accumulate those Social Security credits, generally someone would have to be paying FICA taxes on that income. The FICA taxes would be $918 on $6K of income.