The mechanical stretching of single polyproteins is an emerging tool for the study of protein (un)folding, chemical catalysis and polymer physics at the single molecule level. The observed processes, i.e., unfolding or reduction events, are typically considered to be stochastic and by nature are susceptible to be censored by the finite duration of the experiment. A formal analytical and experimental description on the number of observed events under various conditions of practical interest is developed. Rules of thumb are provided to define an optimal experiment protocol duration. Finally, a methodology is described to accurately estimate the real number of stretched molecules based on the number of observed unfolding events. The model-free numerical analysis applied to experimental data confirms that poly-ubiquitin binds at a random position both to the substrate and to the pulling probe.