@Smitty_BCS wrote:
Does the trust need to issue K1s for these distributions since there is no income, gain, etc.
No, not if the trust had neither income nor gain and is only distributing corpus.
However, if there is a loss (capital or ordinary), that loss can typically be passed through to the beneficiaries, via K-1s, on the trust's final return (1041).
[as a side note, are you certain there is an NOL? It is unusual for a trust to have an NOL unless there is some sort of business operation involved, there was a sale of rental (or business) property at a loss, and the like]
