We can insert "sudo()" into our function to bypass any access right or record rule restrictions the logged in user has. Supposing the code looks something like this:

for line in record.order_line:

  to_archive = env['project.task'].search([('sale_line_id','=',line.id)])

  to_archive.write({'active': 0})

We can modify it to the following:

for line in record.order_line:

  to_archive = env['project.task'].search([('sale_line_id','=',line.id)])

  to_archive.sudo().write({'active': 0})