I would think a business person would take your quilt top and allow you to make payments, then work it into their schedule when you are close to finished paying for their services. When you make your last payment you pick up the quilt. It’s actually a pretty good deal for a longarmer because they could quilt it whenever they wanted to, making the scheduling more flexible.
Having said that, I’m not a longarmer, so I don’t really know about their business model.