In my ex-company, there were 2 layoffs with in a span of 1 month. In the 1st layoff, the severance pay package was better than 2nd layoff. Will the employees affected in the 2nd round have any recourse to go back and negotiate for a better severance pay?
It unfortunately happens when a company gets close to becoming insolvent, they first lay off their least valuable employees, giving them a decent severance package as the company still has some money, in the next round of lay offs they fire their better employees, giving them less severance because the company is close to running out of money, and then they go bankrupt, and the best employees that they kept until the end get nothing, possibly not even the salaries they are owed.
And it is legal in most circumstances. For example, if the company made written promises to keep employees and is in breech of those promises, that might be illegal.
Will the employees affected in the 2nd round have any recourse to go back and negotiate for a better severance pay
It is very unlikely, unless (1) union policies establish otherwise, or (2) the employees in the 2nd round inquired of the employer about the severance package offered in the 1st round and the employer's answer was false and misleading.