Set in the far distant reaches of space and time, humanity has advanced to the point where it is now the age of intergalactic colonization. One of these colonies is the "Growing City" of Londonium - a self-sufficient, ever-expanding colony seed city on a barren but habitable planet.

The city is presided over by an AI that evaluates its citizens and directs their growth towards optimal results. From childhood to maturity, the city provides for and nurtures young talent so they may choose whatever future they please, so long as they have been determined to have the capability for it. 

By the age of 16, the city will have determined a human's major prospects and potential and thereby assign their rights and priveleges to them as per their evaluation. Those with great potentials will be given access to the resources within the city whether it be in the form of knowledge, technology or materials but conversely those lacking in it will only see basic provisions supplied to them.  The city is not unkind to them though as these basic provisions are plentiful by today's standards and even physical disabilities will be accommodated for to add to their value. However, they simply cannot be allowed to pursue futures they are unfit for. 

If they have been determined incapable of achieving a role's standard proficiencies then they cannot pursue it. If they have an undesirable genetic mutation then they will be made sterile. If the city does not want what they have to offer, they will not be allowed to offer at all. All they are allowed is to live within their limits.

The majority of the population will find their roles but a small subset will find themselves lacking in future prospects. They can either find a way to live with that or not at all. Out of those that do are those who would surrender their lives to those with bright prospects in hopes that doing so will allow them some measure of fulfillment.

This story centers around a young girl who lacked too much and the prodigious man she begs to take her in. The man himself stands opposed to idea of volunteer slavery but couldn't bring himself to refuse her desperate plea. The value of a single life brings them together but it'll also take them apart in the end.

The plot twist is that the girl was previously a boy and the plot twist in that is the city provided her the means to change herself to make her more appealing as a slave.