Assist.
Ned Stark started the Brotherhood Without Banners.... completely by accident.
In season 1, remember Catelyn Stark went to Kings Landing to tell Ned what she suspected about the Lannisters.
She (rightfully) suspected th
at one of the Lannisters (Cersie) pushed Bran out the window in Winterfell & crippled him..... before they sent an Assassin to ‘finish the job’ on him.
But the Assassin was killed by Bran’s Direwolf (Summer) as he dropped his knife, which Littlefinger later identified as belonging to Tyrion Lannister.
Later on, when King Robert Baratheon went on his wild board hunt (that eventually killed him)…. Ned Stark was sitting on the Iron Throne during his absence….. and some villagers came to complain about
The Mountain, Ser Gregor Clegane… who burned their village & raped their wives…
However, The Mountain (i.e. House Clegane) is the Bannerman of House Lannister.
Therefore, when Littlefinger mentions that he is Tywin's Bannerman.... Ned immediately suspected that Tywin Lannister 'gave the order' & sent the Mountain to pillage Ned’s wife’s homela
nd (the Riverlands).
So Ned Stark sent
Lord Berric Dondarrion to arrest and execute the Mountain & also summoned Tywin Lannister to Kings Landing to answer for his 'crimes of treason'.
Because Tywin actually DID send the Mountain to burn down the small villages in the Riverlands in direct response to Catelyn Stark capturing Tyrion & taking him to the Vale for a trial, when she suspected that the Lannisters had tried to kill Bran 2x twice.
In season 2, the role of Berric Dondarrion was re-cast with a new actor, who wears an eyepatch & has a 'flaming sword':
After failing to catch & kill the Mountain in the Riverlands... Berric & Thoros of Myr formed
The Brotherhood Without Banners around the time when the Lannisters started fighting battles against Robb Stark’s Army in the Riverlands.... after Ned was killed in Kings Landing.
The Brotherhood Without Banners is pretty much a
‘militia group’ working against Lannister interests in the Riverlands.
Their original goal was to protect the smallfolk from any forces preying on them.... regardless of which King or Lord they support.
Since we haven’t seen much of them since Season 3…. not sure what their 'current goals' are now, in Season 6.
- The war with the Starks is over.
- King Robert is dead.
- Robb Stark is dead.
- Ned Stark is dead.
- Tywin Lannister is dead.
- Joffrey Baratheon is dead.
- The Mountain died. (But the Brotherhood may not know that he came back as Robert Strong)
- Not sure if Berric or Thoros is still alive.

- Or even still 'running the show'.

So they basically no longer have a 'purpose' to continue on.
And it seems they have added some
new members since then, who may have comepletely turned the organization into a band of
'renegade ‘outlaws', who NOW prey on the small folk......... instead of protecting them.