Once you have been let go from your job, you are responsible under the law for looking for new work, and your former employer is legally responsible for keeping you whole until you find something comparable to what you had before. The challenge, though, is what if you find something that’s not comparable?
The reality is that it depends on the details. If you find a similar role but the pay may be a few dollars less or the benefits are not quite the same, this will likely still be considered re-employment, and will count towards whatever money your former employer may owe you. If however you can only find something at a minimum wage, or a significant demotion that you have to take in order to simply survive, the law says that no, this minimal income should not be held against you for the purposes of calculating your severance.
The same goes for starting your own business. If you start up a new entrepreneurial venture and become successful, then congratulations! At that point you should not need to rely on your employer’s support because you’re earning your own income. If however your business earnings are minimal, then the court will likely not count it against your severance entitlement.