It doesnt. Buddhahood is only existing as long as he hasnt entered Parinirvana. On the other hand side cessation of suffering is supposed to be permanent so the mindstream is supposed not to begin again / ignorance supposed to not arise again. About this I asked hereviewtopic.php?f=13&t=8168
but no canonical explanation / logical proof seems to be available in this tradition.
The mindstream does not arise again after the parinibanna of an Arahant. The reason is that all ignorance and craving, including craving for become has been removed. Therefore, there is no impetus for the sense bases to arise again after the parinibanna. Because the sense bases do not arise, there is no rebirth, and consciousness (cittas) which arise at those sense bases can not arise again. Therefore, there is no further consciousness, including perception, etc. due to lack of sense bases for the 6 types of consciousness ( eye, ear, nose, tongue, body, and mind ) to arise.