There is at least one instance where being encircled tactically is an advantage: any path between two points in the interior is shorter than the corresponding perimeter. Has this ever actually mattered? Has an army ever found encirclement preferable? No Chesty Puller please.
Examples are medieval sieges, when a small defending force could stand against a large besieging army for long time, sometimes for several years.
In the modern (20 century) wars encirclement is always a disadvantage because modern armies need enormous amount of supplies to continue fighting. For this reason an encircled army cannot hold for long time.
EDIT. In this WWII Disney movie, Alexander de Seversky makes exactly this argument on the strategic level: Germany surrounded by the allies has advantage of short communication lines. But the ideas of this movie are highly controversial:
Especially minutes 40-45.
Discarding city sieges, where encirclement is the idea, in the battlefield there are some examples.
Napoleon started the battle of Leipzig in the middle of the battlefield, and he never avoided the encirclement. He moved his forces to each flank depending of the battle development. Later on in Waterloo (Quatre Bras and Ligny), Napoleon started the battle attacking the middle of the enemy line in order to separate english and prussian forces, neglecting the risk of being encircled.
Caesar in Alesia didn't avoid encirclement, and he fortified himself in order to keep his position sieging the fortress of Alesia.
Alexander in Gaugamela fought an enemy so big that he was innevitable encircled, so he planned the battle expecting being encircled and then he attacked the weakened center of the persian line.