It’s actually not nifal. The verb תִכְבֶּה is qal imperfect, 3rd person feminine singular from כבה. The nifal for this verb is not attested as far as I know, but the corresponding imperfect would have a dagesh in the כ, a qamets underneath it, and no dagesh in the ב, i.e. תִכָּבֶה (tikkāb̲eh) rather than תִכְבֶּה (tik̲beh).
The qal verb in this case has a meaning that can be conveyed using a passive verb in English ("be extinguished"); the active "go out" means approximately the same thing.1 For the qal כבה, BDB gives:
be quenched, extinguished, go out, of fire or lamp
I do see how you perceive a different nuance between the passive and active expressions in English. In either case, though, fire is the subject, it stops burning, and the agent responsible for the cessation of burning is not stated in the immediate context.1 I think the decision about whether to use a passive or active construction in English is a matter of English style.2
In Isaiah 66:24, the lack of focus on agency in the qal תִכְבֶּה is consistent with the other verbs describing the dead bodies of those who rebelled against the LORD:
For their worm shall not die, their fire shall not be quenched, and they shall be an abhorrence to all flesh. (ESV)
The focus is on the status of the bodies rather than on attribution of responsibility for this state. For that we have to look to the wider context.
1. This is because, unlike this Hebrew qal, most available English verbs (e.g. extinguish, quench) are transitive (or, if you prefer, divalent), requiring both a subject and object. (See the Hebrew equivalent in note 3.) The idiomatic "go out" is monovalent so can be presented in the same "voice" as the Hebrew. Short of that, English impersonal passives provide a similar sense.
2. For an example of the word used in a similar sense, see Leviticus 6:5-6 (vv. 12-13 in English). See also, Jeremiah 17:27 and Proverbs 26:20.
3. In this case, Hebrew uses the piel for the transitive meaning that is more unambiguously active in English — "to quench". See, for instance, Isaiah 42:3.