So why if applied force is increased the normal force can't withstand the increased force?
The other answers answer this well.
Also is there any possibility that in a situation the frictional force could always cancel the applied force?
In that case you would need a material (surface) which is infinitely strong.
- If you put a heavy stone on a table, the table applies the normal force to hold it up.
- Put on a heavier stone, and the table applies an even larger normal force to still keep it up.
- Put on a too heavy stone, and the table will apply its largest possible normal force; but since this is not enough the table will break. The limit of the strength of the table material has been reached.
The strength of materials depends on direction, microstructure, composition, density etc. and depends on molecular bonds in the end. The point is simply that everything existing and any material has a strength limit.
Each and every small peek in the close-up image you give have their own individual strength in this horizontal direction (also depending on how far deep into the gaps the objects falls). Summing it all up gives you some large force that they are able to withstand before breaking.
So, even if the bonding would never let go, there would still be a material strength limit where the peeks on the microscopic level simply break apart. This is like glue; the glue bondings with the surface might be stronger than the peeks of the surface material themselves. Then those peeks will break before the glue lets go.