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.

When there is a bias toward more reps there will be a bias away from intensity. In order to get that tenth rep the subject will often make those preceding nine reps as easy as she can possibly make them. The only way to get the tenth rep is to save yourself on the first nine.
There are many ways of saving yourself. One way is to blast off at the beginning of the rep so you can ride momentum through the sticking point. Another way is to lock out at the completion of the rep and get a short reprieve.  Another way is to cut the range of the reps short to do less of the demanding work.  While the preceding reps may be easier that last rep will be a bear. That should be enough to stimulate a change. 
Another way of doing it is to have a bias towards intensity. Make every repetition as difficult as possible. Instead of blasting off at the beginning of the repetition such as the overhead press, lift the weight slowly with uniform speed. About halfway up on the overhead press you will experience serious difficulty. That is the sticking point. Instead of rushing through the sticking point move slowly - like walking through Hell wearing a gasoline suit.

If you do it that way you'll not likely get 10 reps. “Yeah, but I want to go fast”. Towards the end of the set much of your strength will have been dissipated and you cannot create the force necessary to cause injury, plus your muscles are very warmed up by this point. Try going fast then and you might get past that sticking point and just barely achieve another rep. The end result is a safe set and one of very high intensity through the entire set.  

Doing a set in such manner you won't be able to lift quite as much weight. What's a deeper state of fatigue, if you can't budge hundred pounds or if you can't budge 150 pounds? I contend it is the former. 
“Yeah, but I want to lift heavy weights”. There is another protocol called the rest pause. You might want to do a warm-up set before this. You lift a very heavy weight as intensely as you can and complete one repetition and rest and then repeat the sequence for as many reps as you can.  
There are many protocols, and all can produce results if performed correctly.  Whatever the protocol at Austin Personal Training and at New Orleans Fitness Trainers we can help you do it safely and productively.