Someone more qualified than me will probably answer this - but in the meantime :
"Resume Own Navigation" means the pilot will do literally that - resume totally his own navigation to the fix/beacon/whatever. This usually means direct but cannot be assumed to be so.
Therefore, if there is some sort of conflicting or opposite direction traffic, the aircraft will be "locked" onto a "radar heading". This is usually issued by the ATCO and will then ensure the aircraft does not stray in any way, from it's given course, thus ensuring separation.
Hmmmmm make sense?
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"Go around..I say again...go around"