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Tested on QGIS 2.18

I can suggest using Virtual Layer through Layer > Add Layer > Add/Edit Virtual Layer...

Let's assume I have two layers, namely "lines_test" and "polygons"

With using this query you may achieve the result you are looking for. Have I correctly understand you?

SELECT *
FROM polygons, lines_test
WHERE ST_Within(ST_StartPoint(lines_test.geometry), polygons.geometry) OR ST_Within(ST_EndPoint(lines_test.geometry), polygons.geometry)

References:

• Chapter 8. PostGIS Reference | 8.5. Geometry Accessors

• Documentation “Join Attributes by Location” QGIS 2.18