If you did not live in the home and did not use it for personal purposes after you owned it, you can treat it as investment property and deduct a loss, if you have one. Enter it as "other property" not "your home." If you used the home for personal purposes (like, it was your mother's lake house and you vacationed there before selling it) then it is personal property and even though you might have a loss, losses aren't deductible on personal property.
You receive a stepped up basis equal to the FMV on the date your mother died. Why do you think the home sold for less than the fair market value? Generally, FMV is what a willing buyer will pay a willing seller in an open sale. Appraisals and tax assessments are estimates of FMV, but the true FMV for anything is determined by what someone else will pay.
Assuming you sold the home relatively close in time to your mother's death, I would say the sale price determines the FMV. (However, you can subtract the real estate commission and possibly certain legal fees if you pay them, and that will allow you to show a small loss. See publication 523.)
Maybe if you inherited the home some time ago, and the market in that neighborhood has declined due to other market forces, you would have a larger loss. Or, if the appraisal was based on homes taking 30 days on average to sell, and you deliberately priced it low to sell faster, or you priced it low to get a cash buyer instead of waiting for someone to qualify for a mortgage, you could have a loss. (You are not required to hold out for maximum value.). But if I was the IRS, I would want to more closely examine any claim of "loss" when the home was sold shortly after death.
