I am starting up a furniture company. I was working at another furniture company, but they are going out of business. None of their models had patents on them. The newest model has been being sold for 6 years. If I start making these chairs, under a different model name and company name, is it possible for the bankrupt owners to get a design patent and file infringement claims?
Not if they were to file a patent application now.
When patents are examined, the patent Examiner determines whether the claimed invention is new and non-obvious in view of "prior art." In this case, the article itself would be considered prior art assuming it was on sale, publicly displayed and publicly used before any patent application was filed.
For example, 35 USC 102 of the patent code recites:
(a)Novelty; Prior Art.—A person shall be entitled to a patent unless— (1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention
There are some exceptions to certain activities that occur within one year of the patent application being filed, but this would not apply since you indicated that the product has been on sale, in public use and on public display for at least 6 years. Unless a patent application was filed a long time ago (within a year on any public disclosure, public use or offer for sale) then it would not be possible to patent this design now.