Generally…
I can think of three scenarios that govern ownership of professional service work performed while under contract:
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A contracts’ terms and conditions between a company and a design services company would stipulate degree of ownership of work performed under the contract. I’ve reviewed a lot of design work contracts and not one of them was limited to ownership of the works’ final embodiment but rather included all the work performed under the contract.
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A non-disclosure agreement is often the first “contract” signed between companies and certainly will include clauses on ownership of work performed. An NDA is general service performance oriented, not specific project related.
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Federal legislation regarding ownership of intellectual property generated from contract service work would apply. Unfortunately, IP legislation is very commonly modified by governments, so what applies today is different several years from now.
The nature of your question is a very difficult area; however, considering the plethora of contract creative service work extant throughout the world, this is a well exercised field. It would be extremely bad form to reuse an abandoned concept between different companies. Taking inspiration from previous work and developing iterative design concept from previous abandoned work would be completely legitimate, and very common practice. This feeds into other discussion thread about “are unused concepts a waste?”