Gomoku, is it possible to not be able to make a legal move?
Yes, it is possible for such a condition to happen, though I'm not sure what you mean by "force." It is possible because it is possible to create a board-state in which neither player has won the game, but the entire board is filled. A simple example of such a state is the following: imagine a filled 11x12 which follows the pattern:

WWBBWWBBWWBB

BBWWBBWWBBWW

WWBBWWBBWWBB

BBWWBBWWBBWW


Obviously, neither player has won the game, and since white and black each have an equal number of stones on the board, it is not impossible to reach such a board state. I have therefore shown that it is possible to reach a board-state in which one player cannot make a legal move. You can also show this for non-full boards by applying the rule of three and three and the rule of four and four.