catutthaṃ jhānaṃ samāpannassa assāsapassāsā niruddhā honti
The Sanskrit root rudh √रुध्, also means to restrain (RV.); not just to stop.
Nirodha in AVŚ. has the signification of holding back; refusing to hand over or share.
In ChUp, it has the meaning of a closed door (an opening in for the knowers, and a closing out for the ignorants).
MBh (3-4-12-13-14) has to be checked for accurate dates; but a general meaning of: restraint, check, control, suppression, destruction, has pervaded throughout the text.
So it seems that restrain and control is as much a part of the meaning of nirodha, than stop and suppress.
And it seems more reasonable (in SN 36.11,) that the gradual sinking to a lower level, aka subsiding (vūpasamo - Sk. root शम् śam = pacify, calm, soothe, settle - RV., or be quiet or calm -TBr. & ŚBr.) comes later on (after the restraint - and not after the ceasing?!?).
In other words, the states involved don’t have to cease, but just be restrained, controled, held back; and then pacified, and settled (as unchangeable as possible).
Middle way.
Metta.