Scenario 1:

Given I have a field with type Integer.
When I update the value of that field to '08'
Then the value is saved in the database as a string

Scenario 2:

Given I have a field with type Integer.
When I update the value of that field to '011'
Then the value is saved in the database as 9 (integer)

Observation

reason I've found is in the file: mongoid / lib / mongoid / extensions / integer / conversions.rb

# encoding: utf-8
module Mongoid #:nodoc:
  module Extensions #:nodoc:
    module Integer #:nodoc:
      module Conversions #:nodoc:
        def set(value)
          return nil if value.blank?
          begin
            value.to_s =~ /\./ ? Float(value) : Integer(value)
          rescue
            value
          end
        end
        def get(value)
          value
        end
      end
    end
  end
end

For Scenario 1:

It attempts to pass Integer(value) if that does not work it raises an exception which is rescued and returns the string representation.

For Scenario 2:

It calls Integer(value) which by documentation does the following:

> If arg is a String, when base is omitted or equals to zero,
> radix indicators (0, 0b, and 0x) are honored. In any
> case, strings should be strictly conformed to numeric representation.
> This behavior is different from that of String#to_i. Non string
> values will be converted using to_int, and to_i.