I left home at 16 first to live at a residential college - this was funded by the local authority as they did not have a college local to me offering the course I wanted to do.
Beyond that option, whilst technically she can leave... the world, the benefits system etc, is NOT set up for 16 year olds to live independently of parents or some in loco parentis set up.
Any of the available council funded options would need her to state and prove, or you to agree, that she is not welcome at home or not safe at home - she can't, and you won't, so that's out.
So unless she's actively going to choose to be homeless and sleep rough, which I highly doubt, it isn't going to happen.
I returned home at 17 and became homeless when my relationship with my Mother became impossible and my Fathers position was he was looking after my sister, I was therefore 'your Mothers problem' and he wouldn't do a thing.
I went to a Young Peoples Housing initiative for homeless people under 25. At first living in a communal group home which had support staff and managers on in the day and a security guard at night (not that they did much beyond secure a packet of biscuits and a mug), then in a bedsite owned by the same initiative, by myself - that was pretty awful, if your belongings were not in your hand they were stolen, drugs were everywhere, at any time someone would be dragged out by police or carted out by paramedics and heading out was a nightmare as we were HATED by the local residents too.
At 18 I got a council bedsit, this was back in the late 1990s and the benefits for young people were somewhat better then tbh - however I totally failed to put myself back into college as the college was absolutely NOT equipped for an 18 year old without parents. I repeatedly had to explain I could not have a parent sign this or agree to that or oversee the other, I didn't have any, I lived independently. Perhaps things are better now, but it is unlikely.
Realistically, if you don't facilitate this, it can't happen, unless as I say, she wants to be homeless which I would put money on she does not. If she does try it, let her do the running, let her find out for herself. It may be that she would be better off going away to college, if theres a course that would suit, but the other options are dire and I would absolutely not recommend them!