Okay, a little context. In games like Crusader Kings and Europa Unniversalis, you can send someone to a country to try and fabricate a claim on a province. Once the claim is fabricated, you can use that as an excuse for war.
So, I was wondering whether or not this is just a mechanic or if it actually happened in the past.
The most famous fabrication that I can think of would be the Donation of Constantine, which basically gave the Papacy a fraudulent claim to being the rightful successor of the whole Western Roman Empire.
This is a bit more controversial, but George Garnett claims in The Norman Conquest: A Very Short Introduction that the Norman claim to England (i.e., that Edward the Confessor promised the kingdom of William) was entirely fraudulent.
I don't have my notes to hand to pick apart a case-study, so I'll offer a different, more theoretical, perspective.
Your right (iure) is incredibly important in an argument or war. You might stake this right through kinship (succession, marriage), legal (for example, having been dispossessed of your territory illicitly), etc. but the most important thing is that you possess a publicly acknowledged or, ex post facto, publicly defensible right to the land. There is little distinction between claims (beyond strong and weak) in CK.
Could a claim be fabricated, certainly. How do we define fabrication? All it might mean is '(the act of) making'. The way you phrase your question attaches negative connotations (fabricating a 'made up' claim - a lie). This would not necessarily have to be the case. It might be uncovering a distant ancestor (although genealogies were subject to forgery, on occasion), or simply creating a plausible and publicly permissible right in that territory. Forging would have held a much more explicit meaning, if this was the intention, although that would be difficult to sustain in the muddy oral-witness culture of the 800s-c.1200.