Uninflected words are called avyaya (“unchanging”). In the Paṇinian system, they are treated like a kind of subanta, which makes them a type of pada:
सुप्तिङन्तं पदम्। १.४.१४
suptiṅantaṃ padam (1.4.14)
That which ends in sup or tiṅ [is called] a pada (word).
Although it may seem strange that an avyaya is treated as a subanta, doing so simplifies some other aspects of the grammar. Let's see how the system models avyayas.
What is an avyaya?
The avyaya is a large category that includes many different kinds of terms:
The words in the list beginning with svar, as well as a nipāta, are called avyaya.
taddhitaḥ ca a-sarva-vibhaktiḥ
Likewise for taddhita suffixes not used in all vibhaktis;
krt suffixes that end in m or an ec vowel;
the suffixes tvā, tosu̐n, and kasu̐n;
and the avyayībhāva.
svarādi refers to a list of words in the Gaṇapāṭha, one of the secondary texts used with the Aṣṭādhyāyī. The svarādi list includes words like svar, antar, and hyas, among many others. nipāta refers to a subtype of avyaya that includes words like ca, pra, and so on.
The other rules are more straightforward:
Rule 1.1.38 refers to various minor taddhita suffixes, as used for words like tatra and tadā.
Rule 1.1.39 refers to various minor kṛt suffixes. The most common of these is the suffix tumu̐n, as in gantum (“to go”).
Rule 1.1.40 refers to the common suffix ktvā and a few minor suffixes used mainly in Vedic works.
Rule 1.1.41 refers to the avyayībhāva, a type of compound.
How do we derive an avyaya?
Since an avyaya is a prātipadika, we first add a sup affix. We then immediately replace it with the luk suffix by 2.4.82:
After an avyaya, āp and sup [are replaced with luk].
And luk will then cause lopa of the sup affix: