It might not make sense intellectually, but as far as the game is concerned, one character losing does not necessarily mean a character on the other side will win.
I'm not saying it is. Lets get it into a timing stack then - as you see it, correct me if I'm wrong.
Companion A (with text "When A wins a skirmish involving [qualifier], draw a card") skirmishes Minion B (which matches the [qualifier]).
1. FP player announces an action (for 1 twilight) that wounds Minion B (lets assume B has 1 vitatlity).
2. Opportunity to play "is about to add twilight" effects.
3. FP player adds 1 twilight to twilight pool.
4. Opportunity to play "when [qualifier] is played".
5. Opportunity to play "is about to take wound" effects.
6. Wound is placed on the Minion B.
7. Opportunity to play "when wounded" effects.
7.1. Character death triggers as a required action.
7.2. Opportunity to play "is about to be killed/discarded" effects.
7.3. Minion is killed and placed in discard pile.
7.4. Opportunity to play "when is killed/discarded" and "when minion B loses skirmish" effects.
7.4.1. Skirmish resolves as a required action, involved in skirmish = "Companion A" (no "Minion B"), winning side = "Companion A".
7.4.2. Opportunity to play "is about to win/lose skirmish" effects.
7.4.3. Companion A is "winning", and there is 0 characters on the losing side.
7.4.4. Opportunity to play "when wins/loses skirmish".
7.4.5. Skirmish resolving finishes.
7.4. Character death action finishes.
8. The wounding action finishes, if it was coming from an event, it's placed in the discard pile
Please note then, in point 7.4.4, when Companion A is considered "winning", the "involved" group contains only "Companion A", as at the point when the "involved" group was created the Minion B was already in discard. Hence you can't play that trigger.