This recently happened to me which ended up being the best "seat swap" I have ever had. On a EWR to SFO flight my PPs didn't clear (of course) and I went to take my original seat. Per usual I boarded late to find a women in my seat with my same seat assignment. I walked back to the FA told her what was going. She then seat me out the jetway to the GA. The GA was initially pretty freaked, as was I as I was told the flight was filled, but somehow the GA came up with a F lie flat seat and cleared my PPs. All well that ends well.
I guess this would be another reason as to why to board early (I don't) per other above comments, he who has possession of the seat first may ultimately be the one who keeps the seat. I could have ended up being bumped to the next flight had the GA not found a seat for me.