@Lamarcus Stephenson - it depends on your area. In mine there is a set of usual and customary closing costs that each party is responsible for. For example, we have transfer stamps which can be about $8k - $10k and there is a set breakdown of who pays for what
What does the original contract say regarding who pays closing costs? Your assignment should reflect the original agreed upon terms.
The answer to who pays closing costs should already be in the purchase contract.
Not sure why the end buyer sending the signed contract back to you would be taken as a sign that he's not going to pay the closing costs if the contract says he's supposed to. Have you asked him why he sent it to you? What did you tell him to do with the contract once he signed it? Maybe he just sent it to you so you can deliver it to whoever will be handling the closing/escrow on the deal.
Too many unknowns for us to answer the question. Bottom line, read your contract and - if you still have questions - talk to your buyer.
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