If all of an Attacker's characters are sent home, or discarded, etc. and there are no Attacking characters left, does the conflict end without resolution then and there, or does it count as a Defender's victory?

Conflicts only end after both players pass consecutively.
If the defender's action removes the attacker's last character, the attacker can use their action to move in a character, or play a character from their hand into the conflict.

I get that. But if there are still no Attacking characters left when both players pass, what does that mean?

Attacker will have 0 skill total.

https://fiveringsdb.com/rules/reference#3-2-3-compare-skill-values-and-determine-result

First, determine the attacking player's total skill in the conflict by adding together the skill (that matches the conflict type) of each ready attacking character and factor in all active modifiers. Then determine the defending player's total skill in the conflict by adding together the skill (that matches the conflict type) of each ready defending character and factor in all active modifiers.

The player whose side has the higher total skill wins the conflict. In order to win a conflict, a player must count a total skill of 1 or higher. In the case of a tie, the conflict is won by the attacking player. If both players count 0 skill, the conflict resolves with no winner, and the ring is returned to the pool of unclaimed rings.

Thank you.