If you were laid off today in MA you may be able to collect unemployment concurrently with your severance. Below is the language from MA.gov.
"If you were required to sign what is known as a "release of claims" as a condition of receiving severance pay, the severance pay would not be disqualifying."
A release of claims is a standard document that says that you won't sue the company and won't speak disparagingly about the company and is a condition of receiving your severance package.
If you signed such a document then get your unemployment application in ASAP.