DHS take away benefits?

Will The Department Of Human Services take away my benefits (Food Stamps and TANF) if I have over $1,000 in my bank account. When you apply for the benefits they ask for your account numbers for your checking and savings account. Someone once told me make sure you have less than $1,000 dollars otherwise they will deny you! How true is this. I mean everyone has to save to get ahead. If I don't have money saved what do they expect me to do if my car breaks down or what not? Any information on this would be great!