Can a lender come after you after foreclosure?
If your home sells for less than you owe, some states let the lender sue you for the difference (a "deficiency judgment") and some don't. Pick your state to see the rule where you live. This is general information, not legal advice.
The shortfall after the sale
Say you owe $250,000 and the home sells at foreclosure for $210,000. That $40,000 gap is the "deficiency." In some states the lender can get a court judgment for it and try to collect; in others, anti-deficiency laws bar or limit that, especially on a primary residence or an original purchase-money loan. Many states also apply a "fair market value" offset so you're credited the home's real value, not just a low sale price. The rules are condition-specific, so use this as a starting point and confirm with an attorney.