There is no such requirement of staying in any place for an Arhant.
An Arhath doesn't valueBut the same things as you or me. Ifsutta you read the text carefully, the Arhath didn't even value the bare necessities to maintain a living. Thisrefer is because the value of worldly possessions are no longer of any value to him. Instead he chose to stay closespecifically related to the place which helped him attain Nibbanavanapattha paryaya (monastic practice).
This might be difficult to understand because Where the mindset of an Arahath is quite differentDhamma practitioner feels that s/his mindfulness becomes established, their mind becomes immersed in samādhi, their defilements comes to ours. To take an exampleend, you have a choice to stay homeit means the place is suitable and studyhelpful for an exam or to go out with your friends. Which would you choose? You always choose what is most valuablethe person to youarrive at Nirvana. In a similar mannerSuch places should not be left, this Arhath has chosen to stay closeas one needs every bit oh help that they can get in order to become an Arhant. If the place he attained Nibbanasurroundings are helping, instead of moving to a place which could have been much easier to livesuch surroundings should not be left.
You may wonder what about all the BhikkusThe sutta does not describe an Arhant, rather someone who visited many places taking the message of Dhamma. An Arhath with never think twice about helping others to attain Nibbana and end their suffering. This is why Lord Budhdha instructed Bhikkus to walkyet to every corner of the world and spread the message of Dhamma. Apparently an Arhath is a Kalyana Mithra (a friend who help you understand Dhamma and attain Nibbana)obtain enlightenment.