This is a hard concept for a lot of people to grasp. Many of us are very rigid in our approach to our training (and life). We have a hard workout to crush- we go and crush it. Even if we only slept 5 hours the night before, didn't eat enough pre workout, and had our schedule thrown off because of a emergency or change in the schedule (gotta love last minute client reschedules!). That's not to say we shouldn't be able to push through situations and make stuff work. I am talking about it would more detrimental for us to stick to plan A and not adapt.
We see this concept of being flexible and being able to adapt in the world of training all the time now. The concept of Autoregulation (making judgement calls during the training session on how much to push or back off) is a perfect example. Tons of technology like HRV and jump tests show an athletes readiness pre-training, allowing coaches to adjust and dial in the workout. Coaches like Dan Pfaff (https://www.youtube.com/watch?v=3COzfyucuns) and Joe Kenn ("Be the most adaptable coach in the building!") are known for pushing a Plan B, and even C! When I got to speak to Coach Pfaff during some of their on track practices he made this very clear and changed a few of the athletes that day based on their warm ups...
Knowing when to back off is the tough part though. Some of this things (autoreg, technology, your own coach, feedback from the athlete) can help- but you really can't know 100%. There are days when friends use HRV technology like the Bioforce that tells them they are really only in good enough conditioning for a recovery day, yet went out and set a squat PR. Same can be said for athletes I've worked with who look great in warm ups and are feeling great that day but look slow and who's technique looks incredible sloppy that day. Point being the only real way you'll know is through experience.
For example in my own training I know I'll tend to push it too hard in the face of fatigue or injury, to the point where I am getting no return on the time I am spending training and probably making it a longer time before I am right enough to get a quality training session in again. If you have an athlete who says they are tired but you know that they said they've been sleeping well and eating a proper performance diet, that they are probably physically ready to go (but as the coach you'll have to guide them to the proper mental state to perform).
As a coach or athlete- have a plan B ready to go if you feel there may be need to switch it up. Use the proper assessment beforehand (questionnaire, conversation, HRV technology, warm up assessment, etc) to assist you. Remember though- using your own experience as an athlete or coach is invaluable in these situations!