John -- I just went through this in December with the avionics shop that did my upgrade. Also went through a nasty one in the 90s with an autopilot installation. The bottom line is whether you were issued a quote or an estimate.
If you have a quote, they are bound to deliver the project for the quoted amounted UNLESS specific changes to the quote were agreed upon by you and them. In those cases, an updated quote or a separate quote for the agreed upon additional work is created. So, if they said it was $50,000 to install A, B and to interface it to C -- they are bound to that price. If they get into the project and find issues, you have no obligation to incur any additional costs -- it was their mistake for under quoting the job.
If you are working under an estimate, it is the wild, wild west. There is nothing binding and their estimate is just that. Hopefully, they kept you informed for the cost of the changes and no big surprises were found.
As an example, my avionics upgrade in December involved upgrading to a dual Aspen setup. My autopilot is capable of doing a single cue flight director. It was not presented on the original quote as being done and when I was asked if I wanted that capability, I received another quote for the additional work -- including parts & labor. My installation was to the penny matching the quotes I was given despite agreeing to additional quoted work.