My mother is 75 years old and wishes to move into her own place. She draws a retirement income and social security. She has around $75,000 in the bank she wants access to for mecical concerns. Because of her savings she can't get into an apartment she can afford. Is there anyway she can give this money to a relative without it being taxed and she will still have access to it if she needs it?

What you are proposing is FRAUD.

If she "gives the money away", but still has access and control of it, then she REALLY is not giving it away, but merely transferring it under false pretenses to qualify for beneifits to which she is not entitled.

That is the legal definition of FRAUD In my opinion (though note that I am NOT an attorney).

BTW, this is REALLY a LEGAL question, NOT a tax question, and it should be posted in the LAW Forum.