I have a client who lives with her mother and is her caregiver. She received a form w-2 for this and federal taxes were withheld. Is this taxable? And if not, what does she do with the w-2, and the taxes that were withheld

Im going to explain this, on your paystub it will usually show how many dependents you are claiming lets say for example on your paystub you are claiming 0 people but i the ended pf the year when you are filing taxes you are showing dependents that will definitely give you  a good refund since your federal tax withhold was 0, vice versa same rule apply if you have 2 dependents on the w2 you will be getting less money back from the IRS ON REFUND BECUASE THEY WERE WITHHOLDING LESS TAXES From you , I hope this answers your questions 

Taxes will be withheld on a w2 regardless on how many depdnest if you have or not