Think a lot will depend on if they make the playoffs, keep the coaches around, etc.
If they crash land here at the end, new coach, etc, I can see him gone. Lots of teams have money to pay him now and he's proven to be healthy. Only a few teams in contention could pay him, and Red Wings were the team that could pay him the most. On a 1 year prove it deal the last pay-check might have been really important along with who was on our roster.
Now other teams will have money, he'll have a better choice of where to play and get paid. Not likely but he can secure his own legacy(more like add to it) going to a team like the Oilers on a 1-year deal and winning big with McDavid/Draisaitl(Not likley but just an example).
If Wings make the playoffs and even play reasonably well, coaches stay put, He could come back on a 2-3 year contract.
I personally move on... and try to focus on accquiring a center capable of playing on a 1st line, doesn't have to be Larkin but can't be much worst.
Think Yzerman has the goods to get him, but not sure Dallas will move on yet. I'd try and get Wyatt Johnston(22yrs/old) with a trade/extension. Not sure the Stars can afford to pay him long-term; they might be the team to keep eyes on the next two years. I'm low-key rooting for them to win (outside of Redwings) so it's easier to justify letting some players go and rebuild/restructure vs continuing the struggle to win it all.