My mother sold her home to my brother (but still resides on the property) He deeded the property in his name, my name, and her name. A short time later my mother obtained a personal loan from CitiFinancial for $6000.00 and they listed this home as collateral, unbeknownst to them that she had sold the home to my brother. The home has no equity being mortgaged potentially now (overvalued) due to market and home values decline. Would this collateral be binding since she had previously sold the home to my brother? She is 65 suffering numerous health problems and bills and is widowed. Could this debt be discharged, is being on a deed considered full ownership?

My mother sold her home to my brother (but still resides on the property) He deeded the property in his name, my name, and her name...Could this debt be discharged, is being on a deed considered full ownership?
You need to know how the property is titled: in whose names, and the type of ownership (check this: Home Buying / Selling, - QuickTips (http://homebuying.about.com/od/marketfactstrends/qt/0207TinCommon.htm)).
Also, did your mother sign a mortgage or deed to secure debt, or similar document? And has it been recorded in the county deed records? It may be that if no lien or mortgage has been signed and filed, the debt is 'unsecured'. You will need a local attorney to review the transaction.

If her name is still on the deed, yes, they can most likely hold this as a valid lien, at least on her share of the property.