Non-qualified stated interest (NQSI) is term used for certain types of bonds that do not have level interest payments ("Contingent Debt Instruments"). IRS pub 1212 defines these terms and explains how to perform calculations but it is not easy reading. My understanding is as follows, but you need someone who knows this stuff unless you have a decent background in bond accounting theory and calculations, and a lot of time to dig in. I have the background but my understanding of the tax accounting for stuff this complicated is imperfect and fully understanding it is not on my bucket list. I'm glad I have a good tax CPA to backstop me. Information is available in search engines. I would advise searching on the bond CUSIP. One thing you can find is the bond or CD issue document (usually many pages, mostly boilerplate), which may be helpful.
NQSI applies to Contingent Debt Instruments. This is a type of bond (frequently a CD) under which the issuer commits to paying part or all of the periodic interest based on a variable formula or set of conditions. For example, a bond might pay 2% Interest semi-annually plus a payment of 3% (periodically or in a lump sum) if the Dow was above 30,000 at the end of the semi-annual period. The 2% is Qualified Stated Interest (QSI) and is generally treated as normal interest income. The issuer is required to develop a schedule of probabilistically expected payments for the variable part based on some objective reasoning or whatever (it may be in the bond issue documents). The expected payment is the NQSI and is included into the OID that appears on the holder's 1099-OID at year end. The ACTUAL payment of the variable part (in my experience reported on 1099-INT) may be greater or less than the NQSI. This difference may appear on the detail materials supplied with the 1099-OID as "overage" or "shortfall," respectively. On mine it is in the same schedule as where NQSI is shown.
To further complicate the situation, the bond may have been issued at a discount with the idea that price will increase as the payments for the conditional portion are accrued. As with normal OID, the IRS wants the holder to pay tax over the life of the instrument instead of deferring it and treating it as a capital gain.
Your friend should not ignore the NQSI because the bond holder may be able to (or may be required to if in the government's favor) use that amount to either (1) adjust the current year income or (2) adjust the basis used to calculate gain(loss) when the security matures or is called or sold. (Whether it's (1) or (2) is prescribed in pub 1212.) The general idea is that at some point you can get back the tax you paid on interest you never got (or pay more if the actual amount is greater). For example, if over the time the security was held, there is a shortfall of actual vs. expected variable payment(s) then the holder will have been taxed on money they never actually received. If so, and the gain(loss) at disposition is a loss, then that portion the of any loss due to actual vs. expected is considered a short term loss. If the actual loss was greater, the remainder is long term. This is all discussed in 1212 but they even refer you to the IRS regs for some details.
Since your friend has not received any money, then there is probably no QSI, and it sounds like there has been no contingent payment either, so it is likely that careful attention will need to be paid to this so that no unnecessary tax is paid or at least eventually it is recouped. Especially if it is a covered security then the brokerage may provide all the calculations, but you may want to check them!