She wasnt madam Pomfrey. Meaning, while she had a general knowledge of various spells, she did not have the expertise in healing specific spells to be able to heal a death wound on a house elf. Their physiology is very different from wizards.
Case Study: Dobby in "Harry Potter and the Deathly Hallows"
Dobby, the house-elf, is fatally injured in "Harry Potter and the Deathly Hallows" when he is stabbed by Bellatrix Lestrange's enchanted knife. The severity of the injury and rapid blood loss make it difficult for Dobby's friends to save him.
None of them can probably heal such a fatal injury Dobby has suffered. In the book Hermione stuffed the beaded bag in her sock to save it. In the film, the snatchers got the beaded bag.
Why did Hermione not help Dobby? It was too late—Dobby was beyond anyone's capacity to save. Hermione had just been tortured by Bellatrix and was in no state to help anyone.
While Dobby's death was arguably the saddest moment in the entire franchise, it's not as if Harry Potter's author just threw his death in there to keep the audience emotionally distraught. His horrific death at the hands of Bellatrix Lestrange was a necessary addition to the story — here's why.
Harry asked if he could help Dobby but he began wailing and talking about how humble he was and how brave he was for facing You-Know-Who twice. Dobby finally told Harry why he was there - he had a warning: he shouldn't go back to Hogwarts School in September because he would be in danger.
When Dobby's last words before dying in Harry's arms are "Such a beautiful place, to be with friends. Dobby is happy to be with his friend, Harry Potter."
According to the WOMBAT test, it is possible that house-elves have an average life expectancy of 200 years, cannot be ordered to kill themselves, breed infrequently and only with their master's permission, can override wizard enchantments, and have an allegiance to their home rather than its inhabitants.
In Harry Potter and the Chamber of Secrets, Dobby is freed from his servitude after Harry tricks his owner, Lucius Malfoy, into gifting him a sock. Dobby wears that sock throughout the rest of the series until his death.
Why didn't Harry use magic to bury Dobby? Dobby was a dear friend to Harry, so he wanted to provide him with a proper burial. Hence, he refused to use magic to bury him.
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After Harry helps him win his freedom from the sinister Malfoy family, Dobby pledges his loyalty to the Hogwarts student. Eventually, he sacrifices himself so that Harry and his friends could go on to save the world from Lord Voldemort.
Dobby broke his promise.
Now it's just tragic, because Dobby returned to save Harry's life one last time and died doing it.
“Master has given Dobby a sock – Dobby is free!”
With just a single line, the character of Dobby the house-elf spawned a million memes that Potterfans have been using for their graduation (and other events) ever since.
Socks are an important symbol for Dobby, who is enslaved by the Malfoy family when we first meet him in Harry Potter and the Chamber of Secrets. At the end of that book, Harry tricks Lucius Malfoy into handing Dobby a sock, thereby freeing him from his servitude.
Dobby frequently demonstrated himself to be immensely powerful, causing Lucius Malfoy himself to back down with just a point of his finger. Kreacher was so powerful that he was able to Disapparate where wizards could not, escaping the Inferi that surrounded the locket Horcrux.
An elf typically claims adulthood and an adult name around the age of 100 and can live to be 750 years old. Elves take their time doing things because of their long life span. So to them 100 years feels like what 20 years feels like to a Human.
Responding to a fan's question of what happened to him after the Harry Potter books ended, Rowling replied with the sad – and actually quite blunt – news that he had passed away. “He died, aged 666” she wrote. Oh. We always thought the Black family's House Elf actually looked older, anyway.
Childhood. Elf mothers are with child for 1 year. Once born, elves' minds and bodies initially grow rapidly, advancing past the infant and toddler stage within the first year. Development then slows down and an elf is mentally in adolescence for roughly the next 49 years.
Where is Dobby buried? Harry is bereft that his loyal friend has passed away and decides to bury him without magic at the beach, just above Shell Cottage. His grave reads, “Here lies Dobby, a Free Elf”. It's a beautiful location, right by the sea!
Dobby first speaks when he greets Harry.
His entrance and first lines are very similar in the book as well, but he adds, "So long has Dobby wanted to meet you, sir," before telling him what an honor it is.
After becoming a free elf, Dobby struggled to find work, as he wanted to be paid. Eventually, he was hired by Albus Dumbledore to work in the kitchens of Hogwarts for a Galleon a week and one day a month off.
Dobby has never been asked to sit down by a wizard. Harry comments, "You can't have met many decent wizards" (2.20). Dobby agrees, and then starts banging his head on the window to punish himself for speaking ill of his family.
The unusual talent known as Parseltongue, which Harry possesses, is passed through a family bloodline. Given that many Dark wizards and witches, including Lord Voldemort, also possess this talent, it is regarded as a dark gift.
Knowing that Harry would be going this year, Dobby decided to protect the one person that meant the most to him by trying to make him feel unwanted by his friends and ultimately disillusioned from going back to school.
“This year, I apologize for killing someone who didn't die during the Battle of Hogwarts, but who laid down his life to save the people who'd win it. I refer, of course, to Dobby the house elf.”