The way you wrote your post suggests that this person is the sole owner of both businesses. If that's the case that narrows down the type of business entity he used for the business to either a sole proprietorship with two different names, a limited liability company (LLC) or a corporation. Which type of entity was the one that went bankrupt and which type is the one you signed your contract with? Is this a development project involving multiple homes, or was yours a single custom build? Was it the old builder that filed bankruptcy, the owner, or both? And what Chapter of the Bankruptcy Code did the business and/or owner file under?
A critical question: does the builder have bond that insures the project will be funded to completion?
In general, if both businesses were/are LLCs or corporations and only Business A filed bankruptcy and not the owner then the new Business B would be able to file bankruptcy, too. But the details matter a lot. If the bankruptcy is a liquidating bankruptcy then the business sells its assets, pays out the creditors in the order specified by the Bankruptcy Code and the Trustee and goes out of business. A lot of small businesses that liquidate and go out of business never file bankruptcy because it doesn't help the business out all that much. Business entities like corporations and LLCs do not get discharges of their debts in bankruptcy like individuals do. The owner of Business B won't want it to go into bankruptcy, too, because serial bankruptcies lead to suppliers, vendors, and large subcontractors avoiding doing business with him. When a lot of them refuse to do business, the guy will need to find a new way to make money because he can't get the services and supplies he needs to be a developer. Multiple failures also deter buyers as well
The large majority of home construction projects I've seen didn't finish their builds on time. That seems to be just a common way business is done. As long as Business B that you contracted with stays in business it's likely to continue to work on the development in the hope of successfully completing the project, which will make doing the next one easier. What all that ends up costing you depends a great deal on what your contract with the developer says.
It might help ease your worry a bit to consult a contract attorney familiar with real estate development projects review your contract and where things stand now and get advice as to what to expect and what you can do to be protect yourself if things go bad. Not knowing and fearing the worst causes more worry and anxiety, in my experience, than knowing exactly what you face and what your options are, even if your options aren't great. Having a plan in place now will help you get the most out of the deal should things go bad.