PlayerA has the longest road, via a long road-chain, like this:
A - - - - - A
PlayerB interrupts that road-chain with a settlement, like so:
A - - B - - - A
PlayerA has now lost Longest Road, because they no longer have an “unbroken road of at least 5 segments”.
Now the question we have is: can PlayerA use Othell Yarwick to move the segments of this now-broken road?
The text of Othell’s card is:
“Remove 1 of your roads from the board and rebuild it for free at a different legal location. The road you remove must only be connected on 1 of its 2 ends to your own pieces. Ignore opponents’ pieces when checking connections.”
...so that means that PlayerA can’t use Othell, right?
(I think I’ve just answered my own question by typing this up, but I wanted to post this question in case others also had it!)