Fan Debbie Sherlock, whose father’s ashes were scattered on the pitch, said it was a “very emotional day”.
She added: “I bought a piece of turf – who knows, my dad might be in it.”
Suzanne Greatrix, whose father’s ashes were also scattered there, said: “My dad first brought me here when I was five-years-old.
“It’s a sad day, but at least it is a chance to say goodbye to the place he loved most.”
The £780,000 cost of the 3G pitch replacement will be partly funded by the club, with £450,000 coming from Bury Council and the Department for Levelling Up contributing £300,000.
Chief executive Neil Sears said there was “a great sense of community” at the club.
He added: “When fans told me that people’s ashes had been scattered I thought it was only right that we recognised them – this is a family club.”
Club officials said the funds would also support a full-time community officer to ensure the new pitch would be used by those who might not normally access health services.
They previously said they wanted to “maximise community usage of the stadium through a diverse number of initiatives, not just football”.
Pitch hire will be limited to 50 hours per week to protect the surface over the next eight years, they added.