This is a really interesting subject. To answer your first question right off the bat, the answer is that while it is certainly not impossible, it is very unlikely. This is largely due to the sheer number and intensity of efforts to locate and/or identity the living (or dead) members of the US military who were categorized either as POWs or as MIA (missing in action.) What makes this so unique is that Vietnam, compared to virtually other American war, had relatively low numbers of soldiers who were unaccounted for. Obviously the numbers were much higher during the Civil War and WWII, but even in the Korean War, almost 8,000 soldiers were declared MIA - a much larger percentage than in Vietnam (2500 MIAs).

And yet, this is a question which has, and, to a certain extent, continues to this day, to captivate the American public. Families of MIA soldiers formed powerful interest groups which lobbied the federal government for decades, securing tens of millions of dollars in funding for continued attempts to locate and/or identity MIA soldiers. Still, as Michael Allen notes in Until the Last Man Comes Home: POWs, MIAs and the Unending Vietnam War, since the 1973 Paris peace agreement, only one living American POW has ever been located in Southeast Asia. (So, to your question, with all the effort and resources put into the POW/MIA recovery effort, coupled with the amount of time that has passed, the idea of an American prisoner still being held in the area seems extremely unlikely.)

Allen argues that this mindset is a function of how Americans dealt with having lost the war in Vietnam. Because of many families' dislike of the anti-war left, many chose not to frame the war itself as a mistake, but rather to believe that soldiers had been betrayed by protesting liberals and weak minded politicians. That betrayal, presumably, carried over into the postwar years, as each attempts to cover for themselves by leaving Americans POWs to rot in Vietnamese prison camps since the 1970s. This put additional pressure on contemporary and future politicians to support the MIA effort, as a failure to do so would be painted as another refusal to support American soldiers. Again, all of this ties back into the US losing the war - a conflict like Korea did not necessitate the same degree of soul searching, because it did not see the United States (still during the Cold War) defeated by a much less powerful and equipped force.

I'd definitely recommend taking a look at the Allen book mentioned above, if this interests you.