We still don't know if or when the 2019-20 NHL season will resume, but given that reports last week indicated that the league was targeting a July return, it's safe to say the playoffs would likely go well into August and maybe even September.
That would mean a very short offseason if the 2020-21 season was still going to start on time in October, but it's looking more and more like the start of next season would in fact be pushed back under such a scenario.
According to a report from The Athletic's Pierre LeBrun, the NHL has discussed the possibility of pushing next season's start back to December. The hope would be to still play a full 82 games, with the regular season likely going into May and the playoffs into July. All-Star weekend and bye weeks would be eliminated and the Christmas holiday break would be shortened.
The report goes on to say that the league may be willing to have this year's postseason run into September or even October. LeBrun reports that he's heard from teams around the league that they would be willing to play this year's playoffs without fans if needed, but that many of them would want to be able to have fans in their arenas before next season could start so they could still make their gate money.
As far as what the rest of this season might look like, Sportsnet's Mark Spector reports that the league continues to push forward with scenarios that include some regular-season games being played before the playoffs -- likely with every team getting to 76 or 78 games instead of the full 82.
If there are no regular-season games, though, Spector says one idea that's getting some traction is for the top six teams in each division to gather in one city, with 1 vs. 2 playing a best-of-3 series to determine the top seed and 3 vs. 6 and 4 vs. 5 playing for the right to continue playing, then the regular divisional playoff format beginning from there.