Why the failure is usually above the roof
The section of a chimney above the roofline is exposed on four sides, has no eave over it and no heated structure around it, and takes every drop of wind driven rain the weather sends at it. Below the roof the same masonry is sheltered, partly inside the building envelope and much warmer. That is why a stack can be crumbling at the top and sound in the attic, and why a partial rebuild from the roofline up is usually what the report calls for.
What a rebuild involves
The failed masonry comes down course by course to material that is sound. Brick is salvaged where it can be and matched where it cannot, because a rebuilt stack in a different brick reads as a repair from the street for the life of the house. It is rebuilt to the original dimensions unless the inspection gives a reason to change them, the flue is reset or relined as the report requires, and it is finished with a new crown, a cap and flashing. Access is scaffolding or a roof platform, never a ladder, and it is a real line in the estimate.
The cost question, answered as far as it can be
A rebuild estimate is built from five things: access and scaffolding, the height and width of the stack, whether the rebuild is partial or full, whether the flue is being relined at the same time, and the brick. No price band is published here, because those five vary more than any figure printed on a page could carry. They are what the written estimate itemizes, and any number given before someone has been on the roof is a guess.
Get a second opinion
A rebuild is the chimney job with the most room between a necessary scope and an aggressive one. The findings are written down with photographs so another company can price the same scope.
Insurance and a rebuild
Where the rebuild follows a storm, an impact, a lightning strike or a chimney fire, there is usually a claim behind it. This business documents the damage with photographs and readings, so you have a complete file to give your insurer. It does not file, adjust or negotiate the claim, and it does not tell a homeowner what a policy will pay before the carrier has said so.
What comes after
A rebuilt stack is new masonry with new mortar, and it goes into the same weather that took the last one down. Waterproofing once it has cured, an annual inspection, and a crown and cap that were built to shed water are what stop the sequence starting again. A chimney that fails early usually failed because a water path at the top stayed open for years.