As I recall Harry and Hermione figured out that the Sword of Gryffindor could be used to destroy a horcrux because it absorbed the Basilisk Venom. The sword absorbs anything that can make it stronger. Does that mean wasn't strong enough to it have destroyed the horcrux prior to killing the Basilisk?
And how did it absorb the poison in the first instance?
I think that the Sword of Gryffindor alone, without its blade being impregnated with Basilisk venom, would not have been able to destroy Horcruxes.
‘It doesn’t have to be a Basilisk fang,’ said Hermione patiently. ‘It has to be something so destructive that the Horcrux can’t repair itself. Basilisk venom only has one antidote, and it’s incredibly rare –’
‘– phoenix tears,’ said Harry, nodding.
‘Exactly,’ said Hermione. ‘Our problem is that there are very few substances as destructive as Basilisk venom, and they’re all dangerous to carry around with you. That’s a problem we’re going to have to solve, though, because ripping, smashing or crushing a Horcrux won’t do the trick. You’ve got to put it beyond magical repair.
Deathly Hallows - page 90 - UK Hardcover - chapter 7, The Ghoul in Pyjamas
So you can't rip, smash or crush a Horcrux; it must be defeated and killed by the delivery of certain substances, one of those substances being Basilisk venom. Without the Basilisk venom, the sword was just a sword -- a precious, Goblin-made sword no doubt, but ultimately just a sword.
As to how the sword became imbued with Basilisk venom, it would seem that Harry, while driving the sword through the head of the Basilisk drove it through a venom sac, exposing the sword to vast quantities of venom. As Basilisks are mythical creatures, I do not know where their venom sacs are located, or if Basilisks have free-roaming venom throughout their bloodstream, hence allowing Harry to bring the sword into contact with venom through the roof of the Basilisk's mouth.
According to Griphook, the sword was originally forged by a goblin known as Ragnuk the First.
Goblin's are capable of both magic and the creation of magical items:
When Rubeus Hagrid visited the Giants, one of the presents he brought was a goblin-wrought helmet which was described as "indestructible".
It's not unreasonable to imagine the sword could be capable of destroying the Horcrux due to a goblin-enchantment, but there is no hint of those powers in the books that I can find reference to. The sword is able to kill the basilisk though, but we don't even know if that was due to an enchantment either.
It is mentioned as well:
Being goblin-made, it has qualities found in only goblin-made artifacts, such as the power to imbibe only that which strengthens it, and repel dirt and other staining substances. As Harry used it to slay a basilisk, the sword was imbued with the basilisk venom, enabling it to destroy Horcruxes as basilisk venom is one of the ways to damage them beyond magical repair.
That is how the sword is able to absorb the poison splashed on the blade via cutting the fang, and thus destroy the horcruxes.
Quotes from Harry Potter Wiki
