FHLMC is also known as Freddie Mac
FNMA is also known as Fannie Mae
both government sponsored enterprises, basically these companies assist in market liquidity. You can purchase homes owned by these corporations, It just means it's distressed (was foreclosed, short sale, Etc.) usually the homes are being sold to cover the cost of the loan/investment amount for the lender. Sometimes great deals and sometimes a lot of work. If you are interested in distressed properties (or any property for that matter) you should find a Real estate agent in your area. If you are in Orange County, Southern California I'd be happy to help, If you are outside my area, feel free and give me a call and I be happy to refer you to one closer to you. Good luck!!
Hope the previous answers gave you an idea of what the FHLMC stands for. It can be confusing. Suffice it to know that it is a government backed/held loan/property that is now (or will be) on market as either an auction or REO property (real estate owned by bank).
I specialize in REO's and all distressed (foreclosures, short sales, auctions) type of properties. Which property exactly are you considering? I'll need an address. I can let you know what it's asking price is, taxes, room dimensions, lot size, etc... and walk you through the buying process. I use to live in the 60647 zip code. Are you looking in Humboldt Park or Logan Square?
I would also recommend you hire a buyers agent to assist you navigate your way through the buying process, especially REO's, short sales, auctions & foreclosures.
A buyers agent will provide you with financial and legal resources, negotiate on your behalf, provide you with market statistics to ensure you don't overpay on a property, ensure that you only pay fair market value, schedule showings of properties for you to see and so much more. A buyers agents' priority is your best interest. Best part is that it's available to you at no charge!
Interview a few agents, start with the ones that responded right here on Trulia, myself included. Once you decide who you feel most comfortable with work with that agent exclusively. Loyalty begets loyalty.