Sutra:
59. iththAl piRarkku sEshamanRenkiRathu.

Meaning:
With this ukAram's avatAraNam, anya sEshatva nivrutti (not being enslaved to another) is being shown.

Sri PBA Swami's Sarartha Deepikai:
There are two types of cases that arise out of the avatAraNam: ayOgavyavaccEtam and anyayOgavyavaccEtam. If a statement is made "the conch has the color white", that is the ayOgavyavaccEtam case. If a statement is made that "the white color is no where but in a conch", then it is the anyayOgavyavaccEtam case. As the second statement is false, the second case cannot be used there. If one says "Arjuna is the only archer", the meaning there is that he has no equal in wielding the bow and therefore the case is anyayOgavyavaccEtam.

In the avatAraNam used for the ukAram, it is the anyayOgavyavaccEtam case that stands. That is, the ukAram shows that the sEshatvam shown to the Lord is only toward Him and cannot be shown anywhere else. Just as "prutviyAm Eva gantha:" shows that the quality of fragrance is present nowhere but in the prutivi (that is, anyayOgavyavaccEtam), so too here it is taken as "jIva: Ayaiva") and that the jIva is enslaved only to Him and no one else.

By the hidden case when it is shown that the soul is enslaved to the Lord, why even bring up the question whether he is enslaved to another and prove that he is not?

In this world, we see that something that is owned by one person is also owned by others. This is seen in the case of a home, a place, a servant, a son, etc. Therefore it is possible that a doubt might come up whether that is the situation between the jIvas and the Lord. To answer that, the case has been taken up and shown that it is not so here.