The significance of treating something as a payment of capital is that you don’t treat it as income first.
Normally, if a claimant receives a regular payment of income, they will use it to live on until they get the next payment and you would only regard them as having any saved capital if there is still some left at the end of the income cycle.
But items that count as capital as soon as they are received (like your TC arrears) do not go through that holding phase: it’s capital the instant you receive it.
But then if you spend it, it is obviously not your capital any more: it’s only capital for as long as you still have it. Just like spending some of your savings that took years to accumulate – once they’re gone they’re gone.
So in conclusion: “treated as capital” just means “not treated as income”. capital used in the HB assessment will always be the amount that the claimant curently has, regardless of where it came from or how long it’s been there.