Here's the problem. If a idea is unfalsifiable,it is a dead end. The classic example of this is Carl Sagan's dragon. Some one claims that they have a dragon in their garage. Steve Novella from the Skeptic's Guide to the Universe described this famous example on Neurologica.
"Sagan also used his dragon analogy to illustrate the logical fallacy known as special pleading – inventing a unique and special reason to explain why each type of evidence that could potentially validate a claim is lacking. There is no reason to speculate ahead of time that the phenomenon in question should have such features, they are just invented ad hoc to explain away the lack of evidence. For example: question: 'Can I see the dragon?' answer: 'No, it’s invisible.' Question: 'Can I feel it?' Answer: 'No, it is non-corporeal.' 'Can I measure the heat of its fiery breath?' 'No, it breathes heatless fire.' Etc."If it can't be falsified, it's just not science. Science works by using evidence to evaluate ideas. If you create a claim that is immune to evidence, it simply is not science.
As a note, it is technically possible for an unfalsifiable claim to be true. It would be extremely unlikely however. Do you think I have a invisible, non-corporeal dragon in my garage?