Yes dogs can sense when they are dying or are on their way to dying.
Some dogs when they know they are dying may go hide somewhere or even wander off somewhere to be alone.
I had a dog that wandered off when I was a kid and I knew he was about to die of old age and I couldn't find him for a few days.
Then I found it out in the woods on our wooded property when I lived on a farm.
I figured he went out somewhere to be alone and that's what he did.
So he knew he was dying and wanted to be alone and outside when he died.
Some dogs do prefer to be alone when they die while others may want you near them when they die.
It's all up to the individual dog as to what they prefer because just like some people like to be alone when they die some pets including dogs prefer to be alone.
But you can try being near the dog when they die and if they try to push you away from them then just leave them alone and let them die in peace.
But some dogs may prefer you to be by their side as often as you can and pet them while they are dying.
Dogs do sense when they are about to die and sometimes will go hide somewhere away from people to be alone and that's okay as well.