Is it permissible to perform the absentee funeral prayer for a deceased who passed away just outside our residential area?
Absentee funeral prayer means a prayer performed in another state from his state of origin.  The sanctioning of absentee funeral prayer can be seen according to a hadith narrated by Abu Hurairah RA:
أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم نَعَى النَّجَاشِيَّ فِي الْيَوْمِ الَّذِي مَاتَ فِيهِ، خَرَجَ إِلَى الْمُصَلَّى، فَصَفَّ بِهِمْ وَكَبَّرَ أَرْبَعًا
“The Prophet gave the people news of the death of the Negus on the day on which he died, took them out to the place of prayer, drew them up in rows and said “God is most great” four times.” 
Imam al-Nawawi explained: “And our madhhab stated the permissibility of performing funeral prayer for a deceased who isn’t in the state. Regardless of whether he is in the direction of the qibla or others. However, the person performing the prayer must face the qibla. And there is no difference as to the distance of the two states, regardless of whether it is near or far and there is no khilaf in this matter wholly for us.” 
If there is something that prevented him from performing the funeral prayer, then it is permissible for him to perform absentee funeral prayer even if the distance is near. Syeikh Zainuddin Al-Malibari said: “If there is a debility that prevented him from attending it (performing the funeral prayer) because he is locked or sick, then it is permissible (for him to perform absentee funeral prayer) according to the opinion (presented by ashab al-wujuh).” 
Thus, whether the deceased is outside or inside his residential area, if the individual who wanted to perform the funeral prayer couldn’t attend it due to various factors, then it is permissible for him to perform the absentee funeral prayer even if the distance is near. Wallahu a’lam.