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Unfortunately, you as an adult child, are not able to claim her benefit. That would only be true if you were a minor. Your mothers spouse (your father) could look into seeing if his benefit is higher now, claiming (her share) of the benefits, although it probably would not raise his much. I'm sorry to give you this information, but adult children are not eligible. I will provide you with a link to the SSA page about survivor benefits.
Best of luck to you. Please follow up with any further questions about this matter.
So what happens to her benefits.
They cease at her death. I'm sorry.
Her survivors are eligible for $255 burial benefits.
Please follow up with any questions you have about this matter.