I've been using Quarn's purge cell buffer mod and it works great, except it seems to purge the enemy AI when you run out the door of a cave so the enemies no longer follow you out.

Does streamline's streampurge do this as well? Or if switch to streamline, can I get purging and enemies that chase you out the door?

set SLh.SLmode to 4 ; Memory Purge Mode (1-6) (Default: 3)
; Lower # = faster, higher # = slower
set SLv.PurgeOnTravel to 0 ; Purge memory on travel & zone?
set SLv.PurgeOnWait to 1 ; Purge memory when character waits?
set SLv.PurgeOnSleep to 1 ; Purge memory when character sleeps?

I don't think so, at least I don't see purges enabled on exit, or load. I also purge on streamsave, but for stability I don't use the automatic event save options. I save often with the hot key or on the timer. You could use this esp just for the save feature. It's quite nice

So, do you get enemies following your character out the door?

I just save the old fashion way. Hit escape and save in a new slot. Then one a week or so I go into my games and clean out saves I no longer need.