I assume the story might go as: "each of the seven kids is allowed out in the world once a week. With each of their names or nicknames being the day of the week when they are allowed to "live"." And then something happens to the child allowed out on Monday?

That's my guess from reading the title and the little description.

Is there anywhere to find out the actual story?

Matt

Spec scripts much harder to come by nowadays. You can read Scriptshadow's assessment of the premise here along with his reactions to all the Black List scripts.

And then something happens to the child allowed to leave on Monday
Motorcycle Accessories

Just read the script. You are correct @i_buy_most_things.

It's a good read, with engaging characters, but the third act and ending is a mess.