My intuition told me that life is too perverse for a simple statement
like "It is the only time in quinella
jai-alai when the losing team stays on the court." to
be true. There had to be an exception.
I found one case right away. In superfectas where 1 or 2 scores
one point, 3 scores one point, then 4 runs it. The 1 or 2 that
the 4 beats for game point stays on the court for the two team
playoff for place and show.
But in any case, I don't think that anyone wants to see 3 team
playoff drag out to seven points. The general trend in the playoff
rules is to get it over quickly and fairly. In the case you mentioned,
I think that it is fair because the eliminated team already lost
to the team with which you would have them rematched in your extended
scenario.