A deficiency judgment is the difference between the amount that the lender receives on a short sale and the amount owed on the property. in most states, the lender has the right to pursue the homeowner to pay that difference. But a "no deficiency judgment" means that the lender is giving up their right to go after the homeowner anytime in the future to collect any additional money.
Some states, like Michigan, have a 6-month redemption period. This is the period immediately following the sheriff's sale (or foreclosure sale) where the homeowner has the right to redeem the proprty for the amount of money that the lender paid at the sheriff's sale. Usually, the lender will pay the full amount that is owed on the mortgage plus late fees and legal cost to purchase back the property. This would be the amount that the homeowner would have to pay to get their property back. But about 30% of the time, the lender will "underbid". That means that the amount that they pay for the house at sheriff's sale is far lower than what is actually owed on the mortgage. In these cases, the homeower can buy back (redeem) their property for that amount. Or, the homeower can sell their property, payoff the lender that smaller "underbid" amount and keep any money that is left over.