If you choose to keep your profile private, Google will simply delete it after July 31, 2011
From the Google+ help section:
“The purpose of Google Profiles is to enable you to manage your online identity. Today, nearly all Google Profiles are public. We believe that using Google Profiles to help people find and connect with you online is how the product is best used. Private profiles don’t allow this, so we have decided to require all profiles to be public.
Keep in mind that your full name and gender are the only required information that will be displayed on your profile; you’ll be able to edit or remove any other information that you don’t want to share.
If you currently have a private profile but you do not wish to make your profile public, you can delete your profile. Or, you can simply do nothing. All private profiles will be deleted after July 31, 2011.”