In our case, the contractor did not complete the work; they abandoned the job twice.
We commenced the work ourselves, with our labor. I have paid a few professionals here and there when necessary, mostly out of pocket. The insurance award has been distributed in part to us by the mortgage company, but they retain more than 1/3 still, as we are not restored/rebuilt yet.
This contractor legitimately did about $2500 of work, after physical damages they caused to our property are deducted (for which I have proof and testimony). We offered to settle for this and they refused, stating they wanted $10k+ because that's what the insurance company paid us, they believe.
There remains no invoice. There only exists an estimate the contractor prepared, which we contested as accurate (as it included much work that either had yet to be performed or was performed by me personally). The contractor acknowledged the errors, asked us to point them all out, said they'd redraft. Yet, as soon as I began to point out the errors, they withdrew communication. When I pressed, including asking for their alleged notes and documentation, and images, to help me determine where the inconsistencies might lie - to reach a viable conclusion and invoice, I was refused until I tossed money at them as "good faith", to the tune of about 1/2 their estimate. This amount was greater than I believed was owed them for all the work they performed, and so I refused and indicated I'd pay them when we had an invoice, perhaps even an accurate one.
Even now, they refuse to respond to my questions presented to their counsel as to whether we have an agreed upon amount legitimately owed. I spent a week (60 hours) going through all my notes, images, memories, and their errant estimate and finally came up with what I believe is an accurate representation of their work. I presented it to them for acknowledgment and consideration and received no response. I then asked whether they'd like to address my conclusions, and received no response.
They'd have been paid for the real work they did, had they provided me an invoice for it. They're after the entire claim the insurance awarded, just because they want it. Thankfully, my mortgage company has the wisdom and likely experience to know that contractors like this exist, and therefore they are in control of the insurance award, so maybe the house might actually get repaired.