According to notations in the 1953 and 1954 Kaiser Motors Corporation Annual Reports, Kaiser Motors (which became Kaiser Industries Corporation in 1955) retained the intangible assets of Kaiser-Frazer Corporation and its subsiduries including Kaiser-Frazer Sales Corporation and all trademarks & patents not required by Willys Motors for the manufacture of automobiles. When Kaiser Industries Corporation was liquidated by a Federal bankruptcy court, the trademarks, logos, etc, of Kaiser-Frazer Corporation went with it. Willys Motors could only purchase fixed assets and tangible inventories of Kaiser Motors (previously known as Kaiser-Frazer Corporation)such as tooling and spare parts inventory.
Because these intangible assets did not go to Willys Motors Chrysler Corporation never acquired them in the first place.
All this was sorted out with Ms. Capri Pilshaw of the Chrysler Corporation legal department back in the 1990's.
To the best of my knowledge and information (not being an attorney or otherwise schooled in the law) the stuff is public domain.