For a non-canon answer, the Star Trek: Destiny trilogy of novels, which takes place about eight years after the events of Nemesis, deals with the final disposition of the Borg (as well as their beginning) in a satisfying way IMHO. I throughly enjoyed these officially licensed novels and highly recommend them, even though they aren't officially considered "Canon”.
EDIT: Spoilers ahead
According to these novels, the highly advanced and xenophobic race, the Caelier, were the birth of the Borg over 4,000 years ago on the other side of the galaxy. A horrific accident had hurled a few Caelier and a few humans back to this time. The ethereal Caelier were badly injured as well as the humans. The last two Caelier went insane and broke with their sacred vows, and forcefully melded with the two remaining humans to stay alive. Thus the birth of the Borg.
Fast forward to about 200-300 years before Picard and Co., a federation starship stumbles upon the non-Borg Caelier, with their captain, Ericka Hernandez. They weren’t allowed to contact home and the crew lived out their natural lives amongst the Caelier in relative comfort except no contact with home. This is when the horrific accident happens. Except for Hernandez, who had befriended a top scientist Caelier, who offered to heal her body and make her young again, by giving her a small injection of Catombs which is what the Caelier were made of (he did this in secret of the others). This allowed her eternal youth and access to their collective thoughts.
Fast forward to “today” with Picard and Co. The Borg are running rampant. They manage to rescue Hernandez and she figures out she can communicate with the Borg. Upon killing the Borg queen, Hernandez steps in and shows them humanity and they all are instantaneously changed to become like the pacifist Caelier “again” and head off to another galaxy.
That’s the story in a nutshell. The Borg weren’t destroyed, but rather forever changed and went away with their Caelier brethren.