The deadline was set by the NHL/NHLPA collective bargaining agreement.
Both restricted free agents are playing in Liiga, the top professional league in Finland. Puljujarvi, a 21-year-old Edmonton Oilers forward, is playing with Karpat; Honka, a 23-year-old Dallas Stars defenseman, is playing with JYP Jyvaskyla.
Each player had requested a trade from his NHL team.
Puljujarvi, selected No. 4 by the Oilers in the 2016 NHL Draft, has 37 points (17 goals, 20 assists) in 139 NHL games, all with Edmonton. He had season-ending hip surgery March 4 and was limited to 46 games in 2018-19, when he had nine points (four goals, five assists).
Honka, a first-round pick (No. 14) by the Stars in the 2014 NHL Draft, has 13 points (two goals, 11 assists) in 87 NHL games, all with Dallas. He was a healthy scratch last season for the final 35 regular-season games and all 13 Stanley Cup Playoff games.
Stars general manager Jim Nill told The Dallas Morning News in comments published Thursday that he'd had trade talks with other teams regarding Honka but wasn't comfortable with what had been offered for the defenseman.