This has to be some kind of post-merger record.
The last coaches fired were in May 2016 and Scott Skiles also resigned that month.
The last coaches hired were June 1st and 2nd, 2016 in Mike D'Antoni and Jeff Hornacek.
We went the entire season without a coaching change for the first time in as long back as I wanted to check which was at least to 1995.
Even wilder, from looking at the teams, it's not implausible we go another season before one happens. The only two I identified potentially are Alvin Gentry if the whole Boogie thing disappoints and perhaps Steve Clifford as he's been there for four years, the longest tenured head coach in franchise history. (Technically he will join Allen Bristow this season if we do that thing where we pretend the first Hornets history is also their history but not the Pelicans history until they move.)
A number of coaches I considered are on teams not expected to win games like Atlanta, Chicago, Indiana, Phoenix, etc. and that puts them in a situation where like Jeff Hornacek who will get a chance to coach without Phil demanding the triangle I figure the teams will just punt until the end of the season especially since most of them are recent hires anyway. (And the Knicks are still paying Derek Fisher for his and Phil's scam.)
Terry Stotts and Dwayne Casey have a good shot at disappointing with their teams but they also just signed extensions.
SVG is still his own boss other than the owner. Doc is no longer so, but like Rick Carlisle I imagine if they intend on retiring especially if the teams disappoint they might ride out the year instead. Especially in Carlisle's case with Dirk being a factor.
Which still leaves whatever it is the Kings do that's called management happening somehow to Joerger.
After the season though I could see a serious massacre like we had a couple years ago where it seemed like half the coaches were dumped. With many similar situations of teams picking up others discarded coaches.
Feel free to place your own bets, especially anyone obvious I missed.