The problem with singing accompanied songs accompanied is when they are sung as if they accompaniment is still being played, and that can make the song sound stilted. The unaccompanied singer, needs to arrange to song for non-accompaniment. From my understanding great folk musicians play along to what they are singing as oppose to sing along to what they are playing and that allows the song to naturally flow.

I use the same technique in music hall - the pianist accompanies what I perform which gives me the freedom to slow down bars, and add pauses for effect. Another technique is borrowing/paying back beats. Paying back - because if add the end of a measure the tune has fallen off the beat, it clashes with our internal metronome and can be uncomfortable to hear. - oh the pain of many Shanty Crew rehearsals!!!!!

Just thinking aloud - are there are discussion threads on singing accompanied songs unaccompanied?