Somewhere in the house there is a folder, or a drawer, holding the paid invoice from the roof, the kitchen and the water heater. The invoice says the job was done and the money went out.
That is the belief: the receipt proves the work was done. It proves you paid one company. It does not show that the company paid the people under it, and it does not show that the city ever signed the work off.
When a folder turns up with no sign-off at all, the fix becomes having a contractor close out an old job that has no final on file. This is what belongs in the folder so it rarely comes to that…