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B is corrent. After foreclosure of the mortgage, the mortgagor has several options. The mortgagor may redeem the property until the foreclosure sale by use of the equitable right of redemption. After the foreclosure sale, the mortgagor may pay off the loan within a statutory period. If these remedies are not used, the mortgagee must return any excess proceeds from the sale. The mortgagor, however, does not otherwise have the right to keep possession of the property after a foreclosure sale whether or not the equity exceeds the amount due on the mortgage.
A is incorrect. After foreclosure of the mortgage, the mortgagor has several options. The mortgagor may redeem the property until the foreclosure sale by use of the equitable right of redemption. After the foreclosure sale, the mortgagor may pay off the loan within a statutory period. If these remedies are not used, the mortgagee must return any excess proceeds from the sale. The mortgagor, however, does not otherwise have the right to keep possession of the property after a foreclosure sale whether or not the equity exceeds the amount due on the mortgage. 
A is incorrect. After foreclosure of the mortgage, the mortgagor has several options. The mortgagor may redeem the property until the foreclosure sale by use of the equitable right of redemption. After the foreclosure sale, the mortgagor may pay off the loan within a statutory period. If these remedies are not used, the mortgagee must return any excess proceeds from the sale. The mortgagor, however, does not otherwise have the right to keep possession of the property after a foreclosure sale whether or not the equity exceeds the amount due on the mortgage. 
D is incorrect. After foreclosure of the mortgage, the mortgagor has several options. The mortgagor may redeem the property until the foreclosure sale by use of the equitable right of redemption. After the foreclosure sale, the mortgagor may pay off the loan within a statutory period. If these remedies are not used, the mortgagee must return any excess proceeds from the sale. The mortgagor, however, does not otherwise have the right to keep possession of the property after a foreclosure sale whether or not the equity exceeds the amount due on the mortgage.