Do every 2 bulls embedded in $ mathbb {R} ^ 4 $ join a compact of $ 3 $?

Leave $ M subset mathbb {R} ^ 4 $ a compact submanifold imbibed diffeomorph for $ T ^ 2 = S ^ 1 times S ^ 1 $.

Is there always a compact subcompact? $ N subset mathbb {R} ^ 4 $ with $ M = N $ partial?

If so, it is $ N $ always a solid bull $ S ^ 1 times D ^ 2 $?