Thanks an0maluas, I found it. Unfortunately replacing the .dta and cache files with backup did not revive PoserPro11 this time. I had to re-install. Luckily, the replaced .dta files DID prevent the need to re-register and enter the serial numbers again.

an0malaus posted at 9:18AM Sat, 13 July 2019 - #4356320

On macOS, they go in /Users/Shared/Library/Application Support/Poser/11/, which is not the same folder as your Poser preferences are stored in, which is the same hierarchy, but under your own username, e.g. /Users//Library/Application Support/Poser/11 or .../Poser Pro/11

In either case, you may need to tell the Finder to show the Library folder, as it's hidden by default, or use the Finder "Go" Menu's Go To Folder option and type in the path.