I'm not sure where you heard this from, but there's no special category of taxes for severance pay.

Note, though, that what will happen is that since this will be paid out in a lump sum, a higher percent of that paycheck will be deducted in taxes. The reason is because the formula for estimating taxes assumes that every paycheck is the same. So if the biweekly paycheck is $4000, the assumption is that you'd make $108,000 on the year. Then when the severance comes, the paycheck is $16,000, which would be interpreted as your partner making $432,000 per year and thus taxed at a much higher rate.

But since that assumption is of course wrong, your partner won't actually end up owing all those taxes at the end of the year, so the overpayment will be returned in the form of a larger refund.