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Basic things to check are: presence of correct device files in will quit the debug shell and continue the boot process at the point it failed.
Of course you will also need to fix the underlying problem and regenerate the initrd so the next boot won't fail again. For the greatest reliability of the upgrade process, you may wish to remove third-party packages from your system before you begin upgrading.
This procedure also assumes your system has been updated to the latest point release of jessie.
For this reason it makes sense to ensure that you will be able to recover if your system should fail to reboot or, for remotely managed systems, fail to bring up networking.
Regardless of the method used for upgrading, it is recommended that you check the status of all packages first, and verify that all packages are in an upgradable state.
The following command will show any packages which have a status of Half-Installed or Failed-Config, and those with any error status.
This way you can ensure that these critical services are running and available through the full upgrade process, and their downtime is reduced.
Although Debian tries to ensure that your system stays bootable at all times, there is always a chance that you may experience problems rebooting your system after the upgrade.