Learn English – Word or phrase for “to create again, but better”

The term lovelorn addresses both the unrequited love and the emotional state of the person whose love is unrequited.

Unhappy because of unrequited love.

Synonyms:

• lovesick
• pining
• languishing
• spurned
• jilted
• rejected
• forsaken

If you are looking for a noun, there is also lovelornness:

The state or fact of being miserable because of unrequited love or unhappiness in love.

I would call the word itself a pet term. This is an interesting topic, and pet terms are probably common within families and other small, tight-knit groups.

An example of this usage, in a headline from a media analysis website:

Limbaugh Explains His Pet Term "New Castrati": Men Who Are "Bullied By Women And The Power Structure And Liberalism"

Note that this is not the same as a term of endearment.

EDIT: This is not an established linguistic term. I consulted a few sociolinguistics textbooks and didn’t find any discussion of this kind of ephemeral in-group language. One place to look would be studies of college slang, like Connie Eble’s Slang and Sociability.

Pet term is also different from pet word, which seems to have a generally accepted meaning: a word that is frequently used or otherwise favored by an individual person or writer. Pet words are already part of the general lexicon, though. Brad Leithauser has a 2013 New Yorker piece about pet words. He gives some examples (sweet for Shakespeare, lad for A.E. Housman) and compares them to stray cats taken in by their users:

Each of these words presents the critic with a little puzzle of devotion: What was it about this particular package of syllables? Why was this stray cat escorted into the author’s studio and offered a saucer of cream and a plump pillow by the fireplace? It’s not as though the studio were soundproof; during working hours, the author no doubt could hear other strays, seemingly no less deserving, meowing clamorously for admission.

Link: Pet Words

So, pet term (rather than word) can convey that it's favored by the in-group, but not established as a true word yet.