Question about unfalsifiability fallacy.

Falsifiability  is a property of a proposition or argument. It means that whatever's been said can be tested against empirical evidence or observation, and can therefore be falsified.

For example, if I say "my username on Logically Fallacious is TrappedPrior", you could verify this by reading my actual username. You would not be able to prove it false, indicating that 'TrappedPrior' is in fact my username. If I say, "my username on Logically Fallacious is FallacyLover69", on the other hand, you would be able to prove it false, so it could not be my username.

An  unfalsifiable  proposition cannot be proven false, because it cannot be tested against empirical evidence. For instance, if I say "my username changes to FallacyLover69 when no one is looking at it". Since the only way to see someone's username is to look at it, there'd be no way to bring evidence against the proposition. Of course, that means there's also no way to bring evidence  for  it either, rendering it unprovable.

A  defeasible  argument is one which, although rationally persuasive, is not deductively valid as it does not completely establish the truth of a claim - that means the premises may provide good support for the conclusion, but it is still possible for the premises to be true and the conclusion false. The relationship between premises and conclusion can be 'defeated' by counterevidence.

A good example of defeasible reasoning would be a rule that has exceptions, e.g. "TrappedPrior checks Logically Fallacious every week" (there are some weeks where I don't).

An  indefeasible  argument would be one that couldn't be overturned by counterevidence...but the concept doesn't appear to have much written about it.

I've read about defeasible and indefeasible evidence in an intro to philosophy book a while back. The whole business is to give an account of justification to the justification condition of knowledge. 

Indefeasible evidence is the kind of evidence that you cannot doubt. Defeasible evidence is the kind of evidence that may be "defeated" by other evidence. 

I think that an unfalsifiable argument has more to do with an error in thinking while the notion of defeasibility is more of a tool in philosophy.