Update on Android 5 Lolipop kills self-signed applications without the possibility of recovery

The essence of the problem:

- If there were applications on the phone that were signed by self-signed cert, then at the time of updating to Lolipop, these applications are deleted.
- If you try to reinstall from the Google Market, the error INSTALL_FAILED_DUPLICATE_PERMISSION -505 gets out

First of all, this concerns air applications: forums.adobe.com/message/6934105
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There is no solution yet.