The pair of restricted free agents needed to sign contracts before Sunday's 5 p.m. ET deadline to be deemed eligible to play any games this campaign.
Both players were seeking trades from the teams that drafted them, but Oilers general manager Ken Holland and Stars GM Jim Nill weren't able to find deals to their liking.
The pair of Finns have been playing overseas in Finland's top pro league and will likely stay there for the remainder of the season. Puljujarvi recently said he intended on staying on home soil, regardless of whether a trade came to fruition. Here's how each player has performed in the Finnish Elite League this year:
Both players signed one-year deals with opt-out clauses in Finland in case either of them was traded to a new NHL club and signed before Dec. 1. Either player could still have his rights traded before the deadline but wouldn't be able to play this season.
Puljujarvi was selected fourth overall by the Oilers at the 2016 draft, while Honka was nabbed 14th overall by the Stars in 2014.