rbt48, It's an interesting question considering that NE is the original top-2 jungle primary state for its legislature. The only difference is that the party affiliation isn't shown on the ballot in NE.
Good point! I can speak to how it works in Nebraska for the state legislature (and other various mayoral and board elections--non-partisan). The May primary lets the top two finishers advance to the November general election. However, even if a candidate gets 99% of the vote in the May primary, they still have to compete in November. If there are only two candidates in the May primary, the same two meet in November! (This has struck me as kind of weird for the 22 years I've lived here.)
If there is a candidate dropout, another can replace that slot by petition with sufficient signatures (not sure how many are require) irrespective of party affiliation, but this needs to occur prior to ~Oct 1st. After that, both candidates remain on the ballot if there is a dropout or death.