I’ve divided a line into 7 segments. I’ve performed other functions. Now I’ve decided I want my line “undivided”. I’ve tried welding the segments but the endpoints are still there.
Welding the edges won’t convert them back to a single edge. It just joins them together basically in the same way an arc’s or circle’s edge segments are joined together. If you want it to be a single edge again you would need to remove the short segments and replace it with a single edge.
What did you do to the edges after the division step? Depending on what you did to it, you may not be able to replace the segments with a single edge.
ctrl z 
… or command z in your case
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Fredo has Remove lonely vertices as part of his tools.
Or you can manually draw in and erase edges to get rid of them.
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I’d forgotten about that in FredoTools. Interestingly it leave the edge identified as a curve. Might not matter in most cases.
Clean up 3 has a feature that repairs divided edges as long as they’re straight. I have a shortcut for that and I use it quite often.
That’s interesting. Technically, a curve is metadata attached to a collection of edges. I could find nothing suggesting that the collection has to contain more than one edge, even though that doesn’t make much sense! I don’t know what this residual zombie curve might affect…
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Nothing. Just went on with other things.
When I erase the segments the adjacent structures erase as well.
The trick given by Box is good but, if you have a lot of divisions, it can take a long time.
Try this:
1 - Draw a line from one end of the divided line.
2 - Do the same at the other end.
3 - Erase all the segments of the divided line.
4 - Draw a new line using the proper endpoints of the 2 lines created in steps 1 and 2. Ideally, these shall be at an angle from the divided line to avoid confusion.
If the edges are used to support a series of faces, erasing the edges will of course result in the loss of other geometry. Even if you replaced the edges with a single edge, any place it intersects with other edges it will get divided again.
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