When you file for unemployment, you will be asked if you are receiving any severance payments. What you should know is that if your severance agreement includes a release of claims, these payments should not count against your unemployment benefits.
You may be initially denied and have to appeal, but you should be able to collect in full after showing your agreement to the DUA.
What you are looking for in the agreement is any language that states you are waiving or releasing legal claims against the employer. This is usually pretty unmistakable, but if you have questions you can consult with an employment lawyer.
This means you should not wait to file for unemployment while you are considering the severance package- your benefits will only date back to the date you filed, so you should get that clock running as soon as you are able, whether or not you ultimately decide to accept the severance package.
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Learn more here about severance packages in Massachusetts.