The phrase "a real word" has no clear definition
The concept of " a real word" is uncertain and its meaning varies between different people. See the answers to what does the phrase "a real word" mean?
"Subjugative" exists in English texts, but is not well attested in dictionaries
"Subjugative" has been used; you note that it is in Wiktionary, and the Google Ngram Viewer and Google Books Search also attest to some usage of this word.
The suffix "-ative" is somewhat productive in modern English as a means of deriving adjectives from verbs (often verbs ending in "-ate"). It has even been attached to English verbs, like "talk". As Tuffy mentions, one issue with using "subjugative" in this context is that it could refer to the entity doing the subjugating rather than the entity that is subjugated (compare "destructive", which describes something that tends to destroy things, not something that tends to be destroyed).
See how "subjugative" is used in the following examples:
By its intervention in the impeachment process, moreover, the Court aborted the possibility that the Congress might reassert the primacy of the equality principle in our governance by condemning President Nixon for his subjugative impositions against political opponents.
(The Constitution in Conflict, by Robert Burt)
Empire, which is the historical culmination of capitalism in the form of a pure hegemonized American political power, has successfully converted and castrated the religions and cultures of Europe and most of Asia. It has been disruptive and subjugative in places like Africa.
("Ummah and Empire", by Mucahit Bilici, in The Blackwell Companion to Contemporary Islamic Thought, edited by Ibrahim Abu-Rabi‘)
The adjective "subjugate" is attested (but it isn't pronounced with "long a")
According to the Oxford English Dictionary (OED), the adjective "subjugate" is pronounced /ˈsəbdʒʊɡət/ or /ˈsəbdʒəɡət/: the vowel in the final syllable is reduced, unlike in the verb. This is similar to the difference in pronunciation between e.g. the verb "desolate" and the adjective "desolate".
There are some adjectives ending in "-ate" that are or can be pronounced with the unreduced "face" vowel (the "long a" vowel), but I think this is not the most common pattern for adjectives like this.
Adjectives ending in "-ate" often coexist with, and may have some overlap in meaning with, past participles or adjectives ending in "-ated", like the word "subjugated" that Lambie mentioned in a comment.
All the same, I wouldn't recommend using "subjugate position"
The OED says "subjugate" as an adjective means "Subjugated; subject to, subordinate" so, since we can say "a subordinate position", it seems logical to suppose that we might be able to say "a subjugate position". And there are a few examples of this phrase that can be found using Google Search, but it seems pretty uncommon, and sounds a bit weird to me.
To my ears, "a position of subjugation to the government" sounds better than either "a subjugative position toward the government" or "a subjugate position toward the government".