Well the fragments vanished from the map as soon as I left clicked Singapore in the base selection window and didn't appear in Singapore. But when I check the parent units OOB button, I see the fragments are still in existence, it's just they no longer have a base, so they're in the nether void somewhere.
I haven't executed the turn yet to see if they reappear, I'll let you know when I do what happens. But obviously this isn't supposed to happen, so I wanted to report it while it was fresh in my memory.
Had I known the 243 squadron was actually a detachment of a squadron in Singapore, I'd have sent it there instead of rebasing it towards India where I was intending to rebuild it later as I thought it was a regular squadron. I'm still learning the OOBs.
Here's a screenshot of the OOB lists for the two units:

Jim