Problem with multilines to singleparts

I'm new here and I have a big problem with clipping - the same is appearing after intersect.
I have a line which is going through one place to be cut in (polygon in the irregular shape)- when I do clip or interesect - it becames out as multiline. And when I explode it, it becames a many small lines, but I want them just to be 2 single parts, not so many single
parts. The demonstration on the jpg
Could anyone help me? I would be really grateful.

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