Can trying to get one extra rep result in the set being less safe and less intense at the same time?
You got nine repetitions the last workout session. You sure would like to get that tenth rep. As a result of getting the extra rep, and as a form of self-protection, the body will make a positive adaptation (become stronger). This is a protocol that works if it's done correctly.
The trouble is, in the process, corners are often cut, and the exercise can become less safe and less intense. If the work is not of a sufficient intensity there is no reason for the body to become stronger. High-intensity work places place demands on the system that require the system to adapt positively to survive.