While “exhaust,” from the Latin for “draw out of,” was first attested in 1540 and went on to a great career in the English vocabulary, “inhaust,” with the meaning “draw into,” was attested in 1547 (something about a “flye inhausted into a mannes throte sodenly”) but soon became obsolete.
You know about “omniscient,” which comes from the Latin for “all knowing,” but did you know there was a counterpart meaning “not knowing”? You can now consider yourself more-scient!
“Exsuscitate” was around in the 1500s, as was “resuscitate,” but where “resuscitate” was for the act of bringing someone back from the dead, “exsuscitate” was for the less impressive act of rousing or waking someone up from sleep. It didn’t stick, and it doesn’t look likely to be resuscitated.
“Postliminary” has a technical use in international law, where it refers to the “right of postliminy” (stuff taken in war gets returned), but it’s also been used sporadically since the early 19th century as the opposite of “preliminary.”
Back in 1600 the word “inaugurate” was used to describe a ceremonial act of consecration or induction into office, but there was also the word “exaugurate” meaning “to cancel the inauguration of; to unhallow, make profane.”