Why do people try to avoid stub in a pcb? Can we foresee the stub in schematic level?
How can we forsee the stub at schematic stage? Wouldn't a stub be known only during placement and routing?


Although you cannot prevent the layouter from adding unwanted stubs to the circuit, you as a circuit designer can forsee such things based on your experience or the type of circuits your are designing (mostly high speed signals). This is also another reason why the designer is involved in the review of a layout, since such things can sometimes be overseen by the layouter if the complexety of the circuit grows.


  What are the issues with having a stub in the signal/current path?


As far as I can say, the main issue with unwanted stub are the creation of uncessary signal reflections, impedance mismatch and antennas when used in conjunction with high-speed signals.
For example:

Impedance matching

At high freuquency, the characteristic of the traces and vias are used to recreate reactances used for matching the impedance of the source an load. If there is some additional stub which was not supposed to be there, it might lead to some mismatch problems.

EMI

Very large dI/dt bouncing up and down in these unwanted stubs can be radiated if the stub length becomes comparable to the wavelength of the signal, according to the following

$$l_{stub} \approx \frac{\lambda \cdot f}{10} $$