I have dealt with young people in the past who have had their own tenancies at 15. They were supported by organisations a lot but they were in their own name. Where they were at risk from their families, had no one else to live with but were considered too "old" to be in care.
Long answer: This may have happened in the distant past but they shouldn't be getting away with it today. They would assess whether there was anyone known to the young person who could offer care - either relatives or friends. They would regard the latter as a private fostering arrangement and in either case they would expect the parent(s) / whoever has parental responsibilty to support the arrangement financially - even if this just meant that the carer claimed benefits for the young person.
If there was no one who would care for the young person then social services would either place them with a foster carer or in a residential home. They might find this hard to do if the young person was sofa surfing with various friends and didn't want to be in care but there is a legal requirement on them to make sure that young person is safe and cared for.
It is possible (but unlikely) that the young person might be offered a residental placement where they effectively have their own flat or bedsit within a communal building but there should be staff on site 24/7. These kind of places are usually just for young people who are above school leaving age and typically they are used to help care leavers prepare for independence.
If you believe social services have placed a 15 year old in a flat on their own please kick up a fuss about it. It shouldn't be happening.
Parents / people with parental responsibilty can't just abandon a 15 year old, even if that 15 year old refuses to return home. They would still need to give consent to plans for that young person's care.
Would social services place a fifteen year old (family won't support them) in a flat alone? Can't post any more details as I don't want to identify the person and it's not local so I can't easily find out. Just concerned and obv don't want to leave something that might not be right.