An attacker with access to the console of the computer and with the ability to reboot the computer can launch a shell (with root permissions) when he/she is prompted for the password to unlock the system partition. The shell is executed in the initrd environment. Obviously, the system partition is encrypted and it is not possible to decrypt it (AFAWK). But other partitions may be not encrypted, and so accessible. Just to mention some exploitation strategies:

Elevation of privilege: Since the boot partition is typically not encrypted: It can be used to store an executable file with the bit SetUID enabled. Which can later be used to escalate privileges by a local user. If the boot is not secured, then it would be possible to replace the kernel and the initrd image.

Information disclosure: It is possible to access all the disks. Although the system partition is encrypted it can be copied to an external device, where it can be later be brute forced. Obviously, it is possible to access to non-encrypted information in other devices.

Denial of service: The attacker can delete the information on all the disks.

The Exploit (PoC)

The attacker just have to press and keep pressing the [Enter] key at the LUKS password prompt until a shell appears, which occurs after 70 seconds approx.

Source: Enter 30 to shell: Cryptsetup Initram Shell [CVE-2016-4484]