The partnership knows the name and address of its partners, and how many units each owns, but does not know whether the account is taxable. So it just sends everybody their K-1, and the partners are supposed to know what if anything to do with it.

I also own units of this partnership, although in a taxable account, and probably not the same number of units as the OP. The Unrelated Business Taxable Income for 2006 is given on my K-1 as a negative number, so OP's should be also.
Therefore his 401K will not be taxed on a basis of this holding.
Can he in any way take a tax advantage for this negative UBTI? In the taxable account, my capital account is reduced because of this and when I dispose of the units I'll get some value out of that negative number. In a taxable account, presumably just that the units will be worth less than had the partnership not had that loss?
If OP holds another partnership with positive UBTI, the negative number here will act as a credit so that the 401k is only taxed if the sum of UBTI's for total partnerships is over $1000? Or will the 401K be taxed if ANY partership has UBTI over $1000?

Best wishes, Chris