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Tested on QGIS 2.18

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

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

With using this query you may achieve the result you are looking for.

SELECT *
FROM polygons
WHERE polygons.id NOT IN (
    SELECT polygons.id
    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:

• PostGIS – Opposite of ST_Within

• Chapter 8. PostGIS Reference | 8.5. Geometry Accessors

• Documentation “Join Attributes by Location” QGIS 2.18

There is a possibility using a "Virtual Layer" through Layer > Add Layer > Add/Edit Virtual Layer...

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

With using this query it is possible to differentiate between line ending within polygon and line passing all the way through polygon.

SELECT *
FROM polygons
WHERE polygons.id NOT IN (
    SELECT polygons.id
    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:

• PostGIS – Opposite of ST_Within
• Chapter 8. PostGIS Reference | 8.5. Geometry Accessors
• Understanding "Join Attributes by Location" in QGIS

Tested on QGIS 2.18

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

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

With using this query you may achieve the result you are looking for.

SELECT *
FROM polygons
WHERE polygons.id NOT IN (
    SELECT polygons.id
    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:

• PostGIS – Opposite of ST_Within

• Chapter 8. PostGIS Reference | 8.5. Geometry Accessors

• Documentation “Join Attributes by Location” QGIS 2.18

Tested on QGIS 2.18

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

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

With using this query you may achieve the result you are looking for.

SELECT *
FROM polygons
WHERE polygons.id NOT IN (
    SELECT polygons.id
    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:

• PostGIS – Opposite of ST_Within

• Chapter 8. PostGIS Reference | 8.5. Geometry Accessors

• Documentation “Join Attributes by Location” QGIS 2.18

Tested on QGIS 2.18

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

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

With using this query you may achieve the result you are looking for.

SELECT *
FROM polygons
WHERE polygons.id NOT IN (
    SELECT polygons.id
    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:

• PostGIS – Opposite of ST_Within

• Chapter 8. PostGIS Reference | 8.5. Geometry Accessors

• Documentation “Join Attributes by Location” QGIS 2.18

Tested on QGIS 2.18

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

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

With using this query you may achieve the result you are looking for.

SELECT *
FROM polygons
WHERE polygons.id NOT IN (
    SELECT polygons.id
    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:

• PostGIS – Opposite of ST_Within

• Chapter 8. PostGIS Reference | 8.5. Geometry Accessors

• Documentation “Join Attributes by Location” QGIS 2.18