Even the most experienced pillion cannot deal with sudden braking if they're holding on to the rider, it will end in full body weight going forward then a swift headbutt and most likely a chip in the back of your crash helmet.
Years ago i used to take people for a spin, or girlfriends that used to love going out on the bike whenever the weather was half decent, but i would never let anyone on unless they used the grab rail, because it locks their body into place whether accelerating or braking.
Add to that i have one of those rubber mesh rear seat covers which are absolutely excellent at stopping them from sliding about at all, well worth the money for such a simple bit of kit.
Worst thing i found with some pillions is that they seemed to have watched too much bike racing on tv, 'cos i'd slightly lean to go into a corner and they would lean as well like a pillion on a sidecar in the TT, but when i was ready to straighten up they were still leaning. It makes the bike go straight instead, to the point of being uncontrollable. This would normally result in a panicked stop and a quick roadside lesson of "Never do that again."
I now explain to people that if you think about the little gadgets lorry drivers have to stop their drinks from tipping over on their dashboard that swivel to keep the drink upright when the vehicle turns, that's similar to how a pillion should ride. As long as their body is in a similar position to the rider, most of any movement will be done around the hip area. It works and gives any new (and probably frightened) pillions half a chance of getting things right first time.