Questions like these are some of the toughest to answer on Avvo.
The problem is that you have a very good question but we cannot see the entire document that could impact the answer.
It would be strongly advisable to spend an hour or two with a local employment law attorney going over your exact severance agreement.
Look for on here: http://www.floridanela.org/members.php
Don't sign it until you do.
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As a general principle, severance packages do not prevent unemployment but they do typically delay payment of benefits because the amount you receive in severance is considered wages. So if you make $1000 a week and your severance package is $10,000 then usually you are ineligible for benefits even though unemploymen may be granted for 10 weeks after which payment of your benefits would start. I do agree that you should speak with an attorney but this is the general legal principle.
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