Output drop/change in linear circuits
Lets say I have a linear circuit with some input and output voltages. Assume this is a block with inputs/outputs. 


You need to tell us whether this is passive or active. (Active means it has powered amplification components.)


  When I connect input of another block to the output of my first block, I observe that my first output will change but I don't want it to change or I want to be able to foresee this change and interfere beforehand to sustain my second block with that original output signal.


You have a couple of options here.


For passive circuits that will not be possible unless the output impedance of the the first is orders of magnitude smaller than the input impedance of the second. This should make any loading effect negligible.
Where active circuitry is used this is usually quite easy. With negative feedback the output will be corrected and the resultant circuit will exhibit a very low output impedance.