certainly take on the only possibly value.
For instance, for the box shown above, the small gray numbers in the unsolved cells represent the possible values. The number 6 is the sole candidate for the bottom left cell and thus is the solution to the unsolved cell.
Sole candidate is the most basic program method to solving Sudoku. My Sudoku program first scans the entire grid for sole candidates and if any is found, the cell is resolved and the possible values for each cell is updated for the affected row, column and box. Then the program looks again for sole candidate. Of course, it may reach a point where no more sole candidates can be found even though the puzzle is still unsolved. That's when more advanced methods are needed.