I experienced a brief period of illness that affected my ability to complete specific exams. Unfortunately, I was not given the opportunity to retake them due to company policy. Friends have told me to say this:
Due to a combination of restructuring within the company and lower demand, my role was made redundant. As I was the last person in, I was the first person out. I am grateful for what I learned and am looking forward to my next opportunity.
Go with honesty.
Lying almost always catches up with you.
Having a short-term bad period is normal and explainable. Just don't make a big deal about it. It isn't about being knocked down, it is about how you get up and back to it.
Focus on going forward and being stable.
If there was a genuine layoff and a genuine LIFO policy which means trainees depart all the time under similar circumstances, then yes just say so - you don't need to explain all the background of what is essentially a routine form of exit.
On the other hand, if this is a lie, and the true cause was illness, then it might be better to simply admit this - especially if the illness was transient and unlikely to be concerning for the next employer, and if it dislodges any suspicion that you were dismissed for capability (such as actually failing the exams, rather than having merely lost the chance to sit them by the vagaries of life events).
Employers may be prejudiced against certain kinds of illness, but they would also be prejudiced against dishonesty and against incompetence if they suspect either, so you would want to think very carefully.
Friends have told me to say this
So your friends have told you to lie.
That's a bad idea. You should ignore advice from these friends.
It is to the point, its a reasonable chain of things to happen so nothing weird there. Those things happen, has nothing to do with you as a person, no red flags. Just some bad timed illness, it happens.
If you subtract "Friends have told me to say this:" from your question, you actually have a pretty good answer too :)
The only thing I might worry about if I was interviewing you, would be the illness. I'm not allowed to ask, but I want to know of said 'illness' is going to come back when I pay you. If relevant you could add a small addendum about it, without telling what the illness actually is. Could be as simple as a "was a bit unlucky, but thats in the past now", or a "it treated now", or a "luckily no longer an issue".
