output

$ ruby -v user_marshal.rb 
ruby 2.2.0p0 (2014-12-25 revision 49005) [x86_64-darwin13]
user_marshaled object
original obj extends:           [Extension, Kernel]
unmarshaled obj extends:        [Kernel]

user_marshal.rb

require 'ostruct'

class Object
  # List modules extended by object
  def extended_modules
    (class << self; self end).included_modules
  end
end

def work(type, original, unmarshaled)
  puts type
  puts "original obj extends:\t\t#{original.extended_modules.inspect}"
  puts "unmarshaled obj extends:\t#{unmarshaled.extended_modules.inspect}"
  puts "\n"
end

class UserMarshaled
  def initialize(name)
    @name = name
  end

  def marshal_dump
    @name
  end

  def marshal_load(arg)
    @name = arg
  end
end

module Extension; end

obj = UserMarshaled.new("object")
obj.extend Extension
unmarshaled_obj = Marshal.load(Marshal.dump(obj))

work("user_marshaled object", obj, unmarshaled_obj)