There is the disclaimer at the end of each of the court shows, that says something about the damages are awarded out of…
I have heard that all funds are paid by te show and nothing is owed by the loser of the trial. If that is the truth, then why would the person who is filed against even put up a fight?
a) they are screened in advance by the show producers. Anyone who appears to be uninterested in arguing their case would be rejected.
b) everyone likes to be told “You’re right, the other person is wrong.” 
Both people are paid from a fund - but the judgement, if any, is deducted from the loser and paid to the winner.
Example: the fund is $5000. Each person would receive half. But the lawsuit is for $2000. The judge awards the plaintiff $2000.
Outside the courtroom, producers hand the plaintiff a check for $4,500 and the defendant a check for $500.
That’s how it worked in the People’s Court Judge Wapner era. I have no idea if it’s universal.