いきなり眠ってしまって焦ったが、大丈夫なようだな。
In this sentence it looks like 焦る probably should be auxiliary verb, since its impossible to do something after one fell asleep. But EDICT doesn't have any such entries. So, is this some expression/unusual usage or what?
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Sign up to join this communityThis 焦る is not a subsidiary verb but is a simple intransitive verb meaning something like "to lose one's cool", "to be flustered". Rather than describing a simple sequence of actions, this te-form is denoting a reason for the following verb. See: te-form (て-form) for Cause or Reason
So いきなり眠ってしまって焦った means either "I was flustered because someone (else) suddenly fell asleep" or "I was flustered because I noticed I had fallen asleep."
According to the dictionary, 焦る may also mean "to panic over something unexpected"
不意のことで動揺し、あわてる意の俗語
https://dictionary.goo.ne.jp/jn/4384/meaning/m1u/焦る/
https://dictionary.goo.ne.jp/word/en/焦る/#je-1040
So the person fell asleep then woke up and panicked, probably thinking it was too late.