Before the fellowship of the ring is even formed at the council of Elrond, the hobbits have a perilous journey getting the ring of power from The Shire to Rivendell. They have to face many dangers in even this short stretch of the road, from the vindictive trees of the old forest, the barrow-wights who envy the living, and of course, the 9 Ringwraiths who pursue them through their entire journey, trying to reclaim the ring for their master Sauron.
Luckily, for most of that journey they had the brave and noble Aragorn to protect them and to guide them as they navigated the many perils ahead, but even Aragorn wasn’t able to prevent Frodo from being stabbed by the Witch King, wielding a Morgul Blade on Weathertop. This wound very nearly costs Frodo his life, sending him through the shadow veil between the living and the wraith world, and even though he survives it, it is something that pains and haunts him for the rest of his days, until he finally makes the decision to journey to the Undying Lands on one of the last ships sailing into the West.
Despite the best efforts of Merry and Pippin, trying to defend Frodo with their barrow-down blades, and even more so Sam Gamgee, who rushes to the side of his dearest friend and tries to limit the damage, the hobbits are unable to save Frodo, and he only survives by the good grace of Aragorn's healing knowledge, and the amazing care and treatment he receives by the magical healing of Elrond in Rivendell.
However, there was potentially another hobbit who may have been able to stop the wound from being initiated in the first place, and that is Frodo’s 'uncle' Bilbo. For once the companions arrive in Rivendell, Bilbo bestows upon his heir the glowing sword Sting, and a very rare and precious Mithril coat of armor, leftover from his own adventuring days. The chain mail was given to him by Thorin, as a sign of their friendship, and in upholding part of the deal of Bilbo’s 14th share of the treasure as the Burglar on the quest.
Mithril is one of the strongest metals in Middle Earth, and was usually reserved for dwarven and elven royalty because of how precious and difficult to obtain it is, so this was a very worthy gift for Frodo to receive. Later in the journey, when the fellowship are ambushed in the dark Mines of Moria, and come up against a hoard of orcs wielding cave trolls, the mail actually does save Frodo’s life and prevent him from being ‘skewered like a wild boar’ by the spear the cave troll thrusts at him.
It therefore stands to reason that if Bilbo had given Frodo the Mithril vest earlier, perhaps when he very first left The Shire, and bequeathed Bag End and many of his possessions to Frodo, he could have prevented the Morgul wound at Weathertop, because Frodo would have been protected by the rare metal. This is also not the only time that the gift prevents serious harm from befalling the small hobbit, and helps him avoid a catastrophe that might have otherwise resulted in his imminent death.
However, it is important to note that an ordinary spear being swung around by a big, brutish cave troll, and an expertly wielded magical blade from Angmar, are two very different things. It is possible that even if Frodo had been wearing the Mithril jacket, he still may have sustained the wound from Weathertop, because the poison of the blade works very differently from most ordinary weapons.
The dark magic imbibed within the sword may still have been able to pierce the thick armor, and even if a tiny shard of the blade had made contact with Frodo’s skin through a gap in the Mithril, it would have resulted in the same outcome of burrowing itself inside his chest, unable to be detected by even one as skilled as Aragorn, and thus would have continued its purpose of turning Frodo to the dark realm.
Undoubtedly though, the Mithril coat would have been better than having no protection at all, and possibly could have made the impact of the wound less severe, meaning that it might have healed better despite the poison and the corruption involved. Perhaps then Frodo wouldn’t have suffered so much, both physically and mentally, as the wound would have always reminded him of the traumas he suffered in Mordor, the terrible allure of the ring of power, and the fact that he succumbed to it at the last moment rather than flowing into the flames as he was meant to.