They don't become taxable as ordinary income.
Once the 'basis' hits zero they become taxable as LTCG.
I'm not addressing the definition of basis as I believe it is complicated and I am not fully sure (however search on the Investor Village MLP board, especially for posts by rock'n'rent).
But I can tell you for sure it becomes taxable as LTCG not ordinary income.
You are correct about it being capital gains. Many publications incorrectly state ordeinary income.
My concern about zero basis has been clarified by consultation with three separate tax attorney's specializing in MLP's. First, , one's adjusted tax basis starts with the ending balance in the capital account shown on the K-1 (assuming being reported on a tax basis, which is almost always the case). No adjustments are to made for suspended losses, differences in depletion and IDC's). To this amount is added your share of partnership debt even if it is classified as non-recourse, which almost always is the case.
Most primers and other literature ignore the debt, presumably because either they don't understand it or they assume that non-recourse debt can't possibly qualify or they believe it is too confusing for the average reader.
Dealer, you are a limited partner and you are going to calculate your share of the MLP's debt and include it in determining your adjusted tax basis in the partnership? I wouldn't think that a limited partner is entitled to do anything with the partnership debt because the LP has no obligation to pay off any part of it.
For a passive investor suspended losses are accumulated until the partnership has income. Then, at the point when the P/S generates income, the suspended losses from prior years can be applied against the partner's share of income for the current year, or some future year.
A general partner can include his share of P/S debt in determining his tax basis in the partnership so that the partner can deduct currently his share of the P/S loss. Without the debt being added in, the GP could not take current deductions in excess of his actual cash investment in the P/S. A partenr can't deduct more than he is at risk for. He is at risk for his cash investment plus his share of the P/S debt if the P/S defaults on its debt.