Does sin result, or is there an obligation to make up the shortened prayers, for one who intended to pray shortened prayers for a specific period, then his stay was prolonged, so he completed his prayers after having shortened them for an additional day?

If the intent of the question is that you resolved to travel and did travel, and then stayed in a certain place during your journey without the intention of staying four days or more, then the ruling of travel is not interrupted by this stay, even if it exceeds four days. And if someone completes the prayer and does not shorten it, their prayer is valid, but they have abandoned the Sunnah (definition) of shortening, and there is no sin upon them.