Let me clear: I did not state any state statute “obligates” an employer to pay severance payments per se. As stated above, if severance is or has been provided to other employees on a discretionary basis, a worker denied severance cannot compel his former employer to pay him such pay legal action.
HOWEVER, under the wage collection statutes (e.g., New York, Maryland, District of Columbia) I have encountered over the years, the salient question turns on whether the severance pay, commissions and/or other forms of deferred remuneration constituted “wages” under the law. Normally, an employee’s right to such compensation vests when the employee does everything required to earn the wages.
IMHO, if the OP here unqualifiedly accrued a week’s worth severance pay for every year he worked for his former employer pursuant to its written policies, then this company would remain obligated to pay him the severance pay just as it would remain obligated to tender his final regular pay check to him under the state’s wage collection law. Consequently, it would appear that the OP has a viable wage collection claim for said severance pay which he should pursue.