My FIL cries in his sleep most of the time and has no memory of what is troubling him.

Let your FIL sleep it out. It's likely he will not remember his nightmare once he wakes up on his own. If his problem continues, have him see his doctor.

Wheredidhego: Speak to his physician about medications.

Play extremely soft music using and echo device or other long playing device. Try melatonin, 5 mg. And if that does not work, 10 mg. It aids resting.

I cry in my sleep a lot. I know what’s troubling me but I will not share with anyone. Obviously you have not earned their trust.

I would mention this to his doctor.

If he has Dementia, he may be having night terrors. My Mom would cry out. I would wake her up, tell her to open her eyes then go back to sleep. IMO, opening your eyes makes the dream disapate. If you think night terrors may be the problem and it happens more than a couple of times a week, talk to his doctor. There is medication for this.

My dad used to do this, but I think in his case, he had been hearing so much about death from within his circle, either via friends or family.
I was living with at one time and his neighbor was found dead by her door inside her home. The police had to break in and discovered her.
That night, he hollered and hollered in his sleep. I had to wake him. I knew what it was.

Be grateful he doesn’t remember and don’t ask him about it, clearly it bothers you more than him. If he has or starts having anxiety that is bothersome to him, talk to his doctor about medication to calm it

I had ultra high anxiety dreams for at least 15 years.
I've always had very cool dreams where I invent all kinds of things,
but these were different.
I finally realized those bad dreams weren't from God.
At night as part of my prayers I started rebuking Satan and all of his demons to stay out of my dreams and to stay away from me.
My bad dreams started subsiding and were completely gone in about a week.
That was over 10 years ago.
Now a bad dream may slip in once every 3 months or so to test me.
But a quick rebuke when I wake up sends that negativity scurrying away.

My point is, there is something you can do.
Pray with him every night.

I can relate to you. My mother doesn’t like to dream. She says she has bad dreams but doesn’t remember what the dreams are.
The brain is very complex and dementia or Alzheimer’s affects sleeping.
We can be grateful they don’t remember. I share your pain and it’s difficult to watch them struggle. Big hug from me to you.
You are not alone 🤗

Nothing you can do about it. It's obviously upsetting to you to observe it, but if he can't even remember it himself, why should you worry about it?
Getting old and at the end of life is not a happy time. This is just how it is.
Thus worry about your own happiness and pleasure in life before you also reach that point.

Let it be then, like a snore.