# Why does limiting friction have to act when a block tied to a wall is pulled?

A block lying on a rough surface, is connected to a wall by a mass less, inextensible string and an unknown amount of force is applied to the block opposite to the side of the wall. Now, if it is given that there is some tension in the string and the block is stationary, does it necessarily imply that limiting static friction is acting? Apparently it does. My question is, if: $$F = f_{limit} + T \rightarrow F = (f_{limit} - c) + (T+c) \rightarrow F = f_n + T_n$$

So why is it not possible that the tension in the string increases to value greater than that when limiting friction acts and the frictional force acting is lesser than the limiting friction ?