I don't know where you have received the understanding about Judges 11:31 because it is not coming from the text. Verse 31 uses the relative and all-purpose preposition 'asher. Strictly translated, it means in this case "that which".
"And it will be that which is going up from the doors of my house..."
Translations of "whoever" are being influenced by that which does come out-- his daughter. I guarantee you that if a beast came out to meet him, it would be translated more consistently as "whatever".
Notice the translations that use "whoever" -- dynamic equivalents like the BBE and CEV, the Catholic Rheims Bible, the NET, and the N/RSV. The ASV, ESV, NASB, and the entire KJV family renders it "that which" or "whatsoever" or "whatever."
So again, I do not know where you are getting this "understanding," but it has no basis in the text.
"then it will be that whatever comes out of the doors of my house to meet me, when I return in peace from the people of Ammon, shall surely be the LORD'S, and I will offer it up as a burnt offering" (Judges 11:31).
The understanding comes from looking at the phrase in which the statement is made and not a single word. You are correct that 'asher is a generic "which," but notice the rest of the phrase:
wehayah hayyotse 'asher yetse middalthe vethi ...
(then it will be) (the one going out) (which) (it will go out) (from the doors of) (my house) ...
- conjunction; verb (Qal perfect) third person masculine singular
- article; verb (Qal active participle) masculine singular
- relative participle
- verb (Qal imperfect) third person masculine singular
- preposition; noun female plural
- noun masculine singular; pronominal suffix first-person neuter singular
It is because hayyotse and yetse are in the masculine instead of neuter form that the statement was made that hayyotse 'asher yetse would be better translated "the one who comes out."