I didn't even realize trades could be made now.
Yeah it's a little unusual for teams to make trades as the playoffs are going on, mostly because there's usually no urgency. But there have been a handful in the past. In another thread, I cobbled together a quick list of trades that were done while the playoffs were happening. Most of them were related to unsigned prospects who were traded away by teams who would lose their rights on June 1st.
But there were some recognizable names like Roman Cechmanek, Brian Boucher, Erik Gudbranson:
May 1, 2000: Kings acquired Steve Passmore from Chicago for a 4th round pick (possibly expansion draft related)
May 23, 2000: Ducks traded unsigned prospect Trent Hunter to the Islanders for a 4th round pick (Anaheim would have lost his rights on June 1)
May 31, 2001: Vancouver acquired rights to (unsigned?) goalie prospect Alex Auld from Florida for 2nd and 3rd round picks (Panthers had a young Roberto Luongo fall into their laps the previous offseason).
June 12, 2002: Philadelphia traded Brian Boucher and a 3rd rounder to Phoenix for Michal Handzus and Robert Esche (the Stanley Cup Final concluded the next day)
May 28, 2003: Kings acquired Roman Cechmanek from Philadelphia for a future 2nd round pick.
May 15, 2007: Boston acquired unsigned draft choice Adam McQuaid from Columbus for a 5th round pick (which eventually became Jamie Benn)
June 4, 2008: Kings traded T.J. Fast to the Blues for a future 5th round pick.
May 13, 2010: Coyotes traded unsigned Jared Staal to the Hurricanes for a 5th round pick (I don't think Phoenix was intending to sign him). Couple more unsigned guys in Jyri Niemi and Mattias Modig were traded before the June 1 deadline that year.
May 8, 2011: Coyotes traded prospect forward Oscar Lindberg to the Rangers for prospect forward Ethan Werek. Werek was a mid-2nd rounder in 2009, but I don't think the Rangers were going to offer him a deal.
June 4, 2012: Penguins acquired the rights to impending UFA Tomas Vokoun from Washington for a 7th round pick.
May 25, 2016: Vancouver acquired Erik Gudbranson from Florida for Jared McCann and a 2nd rounder
April 28, 2017: Chicago traded the rights to impending free agent goalie Scott Darling to Carolina for a 3rd round pick.
May 9, 2017: Kings traded the rights to impending free agent goalie Ben Bishop to Dallas for a 4th round pick. Kings also acquired Boko Imama on the eve of the signing deadline that year.
May 3, 2018: Carolina traded Marcus Kruger to Arizona for Jordan Martinook.
April 30, 2019: Carolina traded unsigned prospect Adam Fox to the Rangers for a pair of 2nd round picks (Fox could have played out his senior year and signed with the Rangers in 2020.)