There are always some irregularities in any conjugation of verb forms in any language. Inuktitut is no different. There are beautiful patterns to see, to be sure, but the underlying structures are not always obvious.
In Inuktitut, there are two basic types for each pronominal ending dependent upon whether the preceding morpheme ends in a vowel or in an allowable consonant in the final position (there are three such consonants in Inuktitut: t, k, and q - ie, all phrases in Inuktitut either end with a vowel or with any one of the three consonants).
1st person, singular, indicative (I am):
[-junga] after morphemes that end with a vowel;
[-tunga] after consonants.
2nd person, singular, indicative (you are):
[-jutit] after vowels;
[-tutit] after consonants.
3rd person, singular indicative (he/she/it is):
[-juq] after vowels;
[-tuq] after consonants.
This type of phonological patterning is simple and elegant (mathematically-speaking) because the variation of the first segment is regular and predictable: /j/ after vowels; /t/ elsewhere. This all happens at the subconscious level and intuitively for native speakers. Before I became aware of it, it never occurred to me that there was such a phonological variation so I think a better way of describing the base pronominal morphemes is - for 'I am' - C+unga, with a capital C to indicate the initial consonant slot. But I digress...
Now, for the first two forms ('I' and 'you') there seem to be no examples of them occurring medially but the third one is definitely allowed by the grammar to occur in the middle of a phrase, but, it seems, only it and not the others.
ikuallak[-tuq] - 'it is (starting to) burn'
ikuallaktuviniq - 'it (started) burning' or 'it burned down', which may be analysed thus:
catch fire + it + past tense
*isiqtungaviniq, because it should come out as isilauqtunga 'I came in' and neither
*isiqtutiviniq because it comes out as isilauqtutit 'you came in'.
The first two pronominal forms cannot occur at middle of a phrase, but the third person form may occur at the middle of a phrase. It's as if the first two forms were "different" from the third insofar as the Inuktitut grammar is concerned.
Now, I think what is happening here (and, I've always maintained) is that the notions of formality and politeness are extended only to the first two ('I' and 'you') and not to 'she/he/it', whose presence is not considered to be obligatory after all. This fact may be enough to put the morphemic class of the third person, indicative, into another grammatical category in much the same fashion as 'it' in English: 'it is sunny out today'.
In other words, the third person singular may act as a purely grammatical function indicating the subject of the sentence - ie, without specifying who or what that is - whereas the first and second person forms always refer to a specific person whose presence or (tacit) acknowledgement is obligatory.
Of course, there are many more pronominal conjugations in Inuktitut for the various case and mood inflections for all the person and number forms. But the /C+uq/ morpheme seems to be the only one allowed to act in the function of a (purely) grammatical subject, and perhaps the only one allowed to occur medially.