I've gotta say I reckon there could be a bunch of managers leaving this season. Let's assume the top 2 are safe but you've then got in the top 4:
-Pochettino a bit moody and could see being tempted by a move abroad
-Lampard personally I consider safe BUT you never know with Abramovich, he is not afraid to pull the trigger and their lack of an elite goalscorer could hurt them
-Ole has a weight of expectation on his shoulders and whilst popular with fans could get found out this season
-Emery needs to find a way of rebuilding, the defence looks weak and he doesn't seem to have figured out how to get the best of his midfield yet
Looking at the other end of the table basically any team under threat of relegation and the knives come out, one thing I've noticed this decade is that even managers who have done a great job getting their team promoted can get the boot if the board feels they have taken the team as far as they can, or they just want a fresh face to try and give a short term boost to get them over the line.
Newcastle is a car crash I need say no more about and tough shoes to fill given Rafa's popularity with fans.
There's a few other teams that could get sucked into it as well.
If you were to turn the question on its head and ask who is untouchable you've basically got:
-Pep
-Klopp
-Nuno
-Howe
-Dyche
Probably about it? But even then who knows if Bournemouth or Burnley got sucked into a relegation scrap. Or alternatively sackings elsewhere opening up opportunities for some of those (I've been saying for a couple of years that Howe needs a stepping stone job, something like an Everton for a couple of years and then a big job, but perhaps he could get lucky and get in at say Spurs directly).