Typically, yes, you can enter into an assignment agreement. Sometimes, it may be more effective to enter into a novation (Terminate and replace the old contract with a new.)
If there is some benefit to the bankruptcy estate being lost, however, the trustee in the bankruptcy case could attempt to avoid the assignment.
One other option might be to simply assume the contract in the bankruptcy, exempt the benefit, and then if there is no objection to the exemption and the assumption is allowed assign the contract afterwards. However, this can be a little bit more complex procedurally.
In any event, the assignment would need to be listed and described on Schedule G and in the Statement of Financial Affairs #10.
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DISCLAIMER - This answer is not legal advice. No attorney-client relationship is formed. The information provided is for educational purposes only. For specific advice regarding your situation, please consult a qualified attorney in your area.