Unaccrued interest is interest you would have been paid if the note reached maturity. That unaccrued interest represents a valid claim that cannot be extinguished in a default. For example, suppose that you are holding an 11% annuity from some company and that company defaults on the annuity. The company cannot claim that their default relieves them of the obligation to pay you this above market interest in the future. You are often entitled to compensation for this unaccrued interest obligation (sometimes so much that I think it is abusive).

COMP 12.3.1R(2) requires the FSCS to quantify compensation for a protected deposit claim at the date the firm is

determined in default and pay compensation comprising the principal sum, interest or premium accrued to that date and unaccrued interest or premium attributable to or arising in respect of the period to the date of default.