PC
Thanks to /u/depreciated_ on reddit for their solution:
Run the following script in Powershell (run as Administrator):
New-NetFirewallRule -DisplayName "Destiny2-Solo-1" -Direction Outbound -LocalPort 1935,3097,3478-3480 -Protocol TCP -Action Block
New-NetFirewallRule -DisplayName "Destiny2-Solo-2" -Direction Outbound -LocalPort 1935,3097,3478-3480 -Protocol UDP -Action Block
New-NetFirewallRule -DisplayName "Destiny2-Solo-3" -Direction Inbound -LocalPort 1935,3097,3478-3480 -Protocol TCP -Action Block
New-NetFirewallRule -DisplayName "Destiny2-Solo-4" -Direction Inbound -LocalPort 1935,3097,3478-3480 -Protocol UDP -Action Block
Write-Host "Destiny 2 Solo mode activated. Press ctl + c to deactivate solo mode."
And then run the following when you are done:
Read-Host
Remove-NetFirewallRule -DisplayName "Destiny2-Solo-1"
Remove-NetFirewallRule -DisplayName "Destiny2-Solo-2"
Remove-NetFirewallRule -DisplayName "Destiny2-Solo-3"
Remove-NetFirewallRule -DisplayName "Destiny2-Solo-4"
This will force the game to block specific network ports, preventing other guardians from joining up in your fireteam. Do note as mentioned in his post that the script needs to be run while your ship is fully in orbit, before starting "matchmaking". After a few minutes, the game will automatically start the strike regardless if others join your team (in this case, won't happen), and you'll be free to play any Strikes solo! This applies to both Nightfall strikes, Nightfall: The Ordeal, any strikes in the Vanguard playlists, or Strikes started manually from each planet's map.
PS4
You can set your time back, preferably 1 hour. This prevents others from matching with you, and you can solo strikes this way. Don't forget to switch your system clock back to normal if you want to play with others again.
I haven't tried doing it with only 4 but with my experience doing it normal I don't believe it's possible. I've tried doing it multiple times after one person has fallen off and keep going with only 5 and it will end up stopping and you can't continue.
There are multiple videos showing how it's possible to skip parts or to do it solo, by using swords and supers to jump the gaps between reactors, but these will only get you to the last area with nothing happening. You have to get to the last plate on each section and have the "reactor temperature rises" message appear for each to actually progress and have the enemies spawn at the final area.
Best Answer
It really depends on the type of activity you are playing. Since a third random player joined you, then you played what you call a matchmaking game type. Matchmaking will pair you up with random players who are also doing the same activity, up to the maximum number of allowed players.
You can tell if an activity is matchmaking by hovering over the icon and viewing the details. If it’s matchmaking, then there will be a line item that indicates as such.
Unfortunately, there is no way to disable matchmaking. You’ll always be paired with other players in matchmaking game types, unless your fire team filled all the allowed slots. The only exception to this is if you’re playing on a console and you don’t have the respective online subscriptions to access the multiplayer features.
You can still do activities with just you and your fire team. Non-matchmaking activities are typically, but not limited to, story missions, side missions, quests, or end game content (which, on average, require more than two people)