The vendor has been working on this since August, and it still is not finished.
If I change the theme, I lose the design, the new design was the goal to begin with. I can't even update the theme, because it will break the site.
apparently anything I do to the site from now n must be done by the vendor. At this point I am ready to have a new theme made that will keep this design and still work like it was supposed to.
The last point first: It is not a necessity that you've to keep the vendor's meter ticking till you keep the site running. Ask for a refund, get it, and get a new vendor to create the theme with same or similar requirements that this bloke worked on. Work with part payments and timeboundness. The present vendor is either milking money out of this never-ending project, or has no knowledge of making a WP theme... Put him in a shitlist if he is still a member here, because imo he is taking undue advantage of your helplessness and is creating blocks in the normal working of a WP site. But weigh all things first and if you're sure that he belongs to the SL, then put him there. I also think that he is only editing and modyfying an existing DEFAULT theme, either WP-default theme or a third-party default theme without having any knowledge of how to create a child theme out of them. Whatever... get rid of him, replace him, and before that, get back your money.
And it will not lose the design if you are changing the theme to see if the site is still working. Change the theme and then add a post with text and image content to it and save it, and see the result. If you see that the post is still published, even without perfect formatting, then the site will work without that problem-theme, and will work with any other theme that's tailor-made to your requirements, imo. If there are custom posts/views, custom homePage, etc. then one might have to recreate them, but the present problem-theme isn't going to be a permenant/unremovable/uneditable block for you. IMO, the vendor must be trying to screw out money from you till eternity by giving you those scary warnings/advices/instructions/whatever about 'changing the theme will destroy the site', etc. He needs a few kicks in the a$$ if he is saying those unprofessional and scary things. A WP site can never get fully destroyed by just removing any normal theme imo.
Even if the site is a e-com site with, for example, woocommerce added to it, the site will not get destroyed if you change the theme. The content lies safe in the database. And it is stored away and safely from all the themes.
Also, you can reinstall the problem-theme once you test the site with another theme and get back to where you were before changing to a test theme... If someone writes a program somewhere that the site gets destroyed if there is a future condition (like changing the theme, etc) then that's one of the most malicious things to do, but in normal circumstances, simply changing a theme WILL NOT destroy a site.
2. A theme will not break a WP site just like that unless the vendor puts some programtic and problematic clauses/functions, just like a timebomb-virus! You can always add another theme and if required change some setting (in css, html, functions, etc.) files to make it look right. All the posts and content are in the database, and the images are in their respective folders, which cannot get lost just like that, if you change a theme!
If he has added custom views posts etc, then it can be a bit difficult to get down to his programming-flow|logic, but that too can be saved and recreated by someone who knows what he is doing...