How do you get a dementia patient to stay seated or in bed when they are a major fall risk?

There are bed alarms that you can use. This would enable you to get to him before he would be able to get out of bed or a chair.
You can place his mattress on the floor. Granted you will have to help him get into and out of bed but the risk of falling is minimized. (If you go this route a Hoyer Lift would be the easiest and safest way to get him up and down)
A Hospital bed at it's lowest position might help. And since this is your home and not a facility you can use bed rails. (Not permitted in facilities as it is considered "confinement")
Stop arguing about it. There is no "winning" an argument with someone that has dementia. He will not remember that you told him not to get up, he will not remember that he got up, he will not remember how he fell or if he fell.

Unfortunately the possibility is high that at some point he will fall and break a leg, arm, hip or concussion that will hospitalize him. Rehab would be the next step and I doubt he would be a candidate for rehab. (sorry to be so blunt)

PS -- My house is essentially one story (guest room/bath upstairs), everyone else downstairs.   Don't kid yourself, falls still happen, depending on your LO

With my Mom I gated her in. I live in a split level and she was on ground level with six steps up to the kitchen. Her bath was there to. Easy excess out of the house. I placed the gate a few inches above the floor so she couldn't climb over it. She would call me when she couldn't get out. No, she didn't like it but my house has 3 flights of stairs. One reason I placed her in an AL to get her on one floor which worked a lot better.

My mom is 101.  We have gotten scripts for meds to help her stay calm and if needed sleeping pills.  I have a pad on the floor that that chimes (like in a store) if she gets up.  I can keep the remote in my room.

My father with vascular dementia first began immediately wanting out of bed as soon as he woke from any nap while in the hospital following a heart attack and stint procedure. I found if I sat in his direct line of vision, this behavior was reduced and if I spoke to him it pretty much didn't happen. Later when he moved to MC, we found using furniture from his home and decorating with photos he recognized reduced the immediate get out of bed reaction and seemed to allow him to better orient himself to where he was and his physical location. The bedside dresser from his home with the dollies and photographs displayed there throughout my parents marriage was very helpful. This might help your FIL for a while, but with dementia there is no good and permanent solution.

You can use motion or bed alarms to let you know when he's getting up and I would consider some significant gate to barricade the stairs. Reaching the wandering stage of dementia is also the point at which many families begin looking into LTC because it's so difficult to provide the same level of 24/7 supervision a facility can.

Blood thinners & falls = serious trouble. It's time to get FIL into Memory Care so he can stay safe(r) since it's a one story building with no stairs and no way to get outside of the premises. You should also get him to the doctor to check him out after this last fall...........you don't know that it looks worse than it actually IS. Internal bleeding can and does easily happen with blood thinners, which is why a CT scan is often warranted after falls.

Good luck!

You can’t. There is no reasoning with dementia. You’d have to use some sort of physical restraint and that can legally be considered elder abuse. Or maybe have his doctor prescribe something to help him sleep all night? I know it’s hard to find a balance of sleeping all night and not being groggy during the day.

This is going to get worse and the next fall could kill him. He needs more monitoring and help than you can give. Please consider memory care?