This is an interesting point you bring, in my opinion. It seems, as suggested in your thought experiment, a piece of energy is lost, menacing the energy conservation principle.
I will try to think of what is happening; trying to rephrase the experiment, let's think in a situation of a given mass, stretched a given distance in a string of constant k. Supposing the mass do not moves at this instant, (having maximal potential and zero kinetic energy) you drop the acid that broke (almost instantaneously) the string. First of all, given the tension of each ring in the string, after the reaction, the potential energy of the system "string+attached body" will "melt together", being left only a kind of residual potential energy associated to the string itself (as strings in laboratory have mass), given the stretched position of each loop.
Now, the tension, specifically the place in the ring where the drop was disposed, we will have a huge torque produced after the "melting", which will force the string to move, eventually very fast. Secondly, the rest of the tension associated with each other ring/loop of the string tends to maintain its movement. If the mass of the string is very small when compared to the body attached to it, the torque produced energy, given the acid disposal beats the residual potential energy that lays in the string and tends to maintain its movement state.