In my experience they don't die when they are out on the trade routes. They just become incapacitated for a while.
I had to change one route because the provisioner kept falling enroute and the supply line would constantly go missing and come back again.
I walked the route myself and could see why.
Egret Tours marina to Jamaica Plains is a dangerous path.
However you can kill them yourself.
One thing to note, if you assign a settler to a supply line they are forever titled Provisioner, even if you later assign them to another duty.
So if the line is still showing perhaps you still have a provisioner on duty.