In Atlanta '96, the US was allowed to field a Handball team, by virtue of being the host nation. Not sure where they dug up the players from, but America’s best and brightest were duly assembled.
The US was, ah… not particularly good at handball, comparatively to the other teams.
Similar to the Nagano Japanese ladies ice hockey team. (They were adorably tiny and polite on the ice, but lost every game. The crowd loved them. I have not followed up to make certain, but I feel pretty sure they have not returned to that sport.)
This year, the US did not manage to send a team for Handball or Rhythmic Gymnastics. I can’t remember for sure but I think they did send someone on rhythmic, we just couldn’t qualify a full team, maybe it’s only the top 10 or 12 countries.