“But in the case of a monk who has attained the cessation of perception & feeling, his bodily fabrications have ceased & subsided, his verbal fabrications ... his mental fabrications have ceased & subsided, his vitality is not exhausted, his heat has not subsided, & his faculties are exceptionally clear”.http://www.accesstoinsight.org/tipitaka ... .than.html
Motivation is a mental fabrication and do not applicable to Arahants.
The existing body of an Arahant was a result of his past Kamma and he/she will live until his past kamma, in regard to body is exhausted.
He/she will live with knowledge (wisdom) without attachment and anger.
He/she will exercise Brahama Viharas.
He may live in a house, temple or under a tree. He is not abide by rules (220 Vinaya rules)