FULL PRODUCT VERSION :
java version "1.8.0_66"
Java(TM) SE Runtime Environment (build 1.8.0_66-b17)
Java HotSpot(TM) Client VM (build 25.66-b17, mixed mode)

ADDITIONAL OS VERSION INFORMATION :
Windows 7 SP1 (64 bit)

A DESCRIPTION OF THE PROBLEM :
When you use the SYSTEM account to install 32 bit JRE on a 64 bit operating system it fails. Here are the relevant lines from the log file:

MSI (s) (4C:18) [10:12:20:607]: ******* RunEngine:
           ******* Product: C:\Windows\system32\config\systemprofile\AppData\LocalLow\Oracle\Java\jre1.8.0_66\jre1.8.0_66.msi
           ******* Action:
           ******* CommandLine: **********
MSI (s) (4C:18) [10:12:20:607]: Note: 1: 2203 2: C:\Windows\system32\config\systemprofile\AppData\LocalLow\Oracle\Java\jre1.8.0_66\jre1.8.0_66.msi 3: -2147287037
MSI (s) (4C:18) [10:12:20:608]: MainEngineThread is returning 3

As you can see from the log file, the installer is trying to run the extracted 32 bit MSI from the 'C:\Windows\system32\...' folder. The issue is that this is a 32 bit install so the MSI gets extracted to the "C:\Windows\SysWOW64\..." folder. Essentially, the installer is trying to run the MSI from the wrong path.

The workaround is to create a front-end wrapper that manually copies the MSI to the 64 bit "C:\Windows\System32\..." path before the install starts. Unfortunately the install takes longer now that the we have to account for this in our wrapper.

As expected, the 64 bit versions of JRE are not affected by this issue. Also worth repeating, this issue only occurs when installing via the SYSTEM account.

REGRESSION. Last worked in version 8u51

ADDITIONAL REGRESSION INFORMATION:
java version "1.8.0_51"
Java(TM) SE Runtime Environment (build 1.8.0_51-b16)
Java HotSpot(TM) Client VM (build 25.51-b03, mixed mode)

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
1. Install the 32 bit version of JRE 1.8.0_66 on Windows 7 x64 using the SYSTEM account.

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
A successful installation
ACTUAL -
The install fails.

ERROR MESSAGES/STACK TRACES THAT OCCUR :
=== Verbose logging started: 1/11/2016 10:12:20 Build type: SHIP UNICODE 5.00.7601.00 Calling process: C:\Packages\6\NEW\Media\jre-8u66-windows-i586.exe ===
MSI (c) (D4:70) [10:12:20:584]: Resetting cached policy values
MSI (c) (D4:70) [10:12:20:584]: Machine policy value 'Debug' is 0
MSI (c) (D4:70) [10:12:20:584]: ******* RunEngine:
           ******* Product: C:\Windows\system32\config\systemprofile\AppData\LocalLow\Oracle\Java\jre1.8.0_66\jre1.8.0_66.msi
           ******* Action:
           ******* CommandLine: **********
MSI (c) (D4:70) [10:12:20:585]: Client-side and UI is none or basic: Running entire install on the server.
MSI (c) (D4:70) [10:12:20:585]: Grabbed execution mutex.
MSI (c) (D4:70) [10:12:20:592]: Cloaking enabled.
MSI (c) (D4:70) [10:12:20:592]: Attempting to enable all disabled privileges before calling Install on Server
MSI (c) (D4:70) [10:12:20:598]: Incrementing counter to disable shutdown. Counter after increment: 0
MSI (s) (4C:F4) [10:12:20:605]: Running installation inside multi-package transaction C:\Windows\system32\config\systemprofile\AppData\LocalLow\Oracle\Java\jre1.8.0_66\jre1.8.0_66.msi
MSI (s) (4C:F4) [10:12:20:605]: Grabbed execution mutex.
MSI (s) (4C:18) [10:12:20:607]: Resetting cached policy values
MSI (s) (4C:18) [10:12:20:607]: Machine policy value 'Debug' is 0
MSI (s) (4C:18) [10:12:20:607]: ******* RunEngine:
           ******* Product: C:\Windows\system32\config\systemprofile\AppData\LocalLow\Oracle\Java\jre1.8.0_66\jre1.8.0_66.msi
           ******* Action:
           ******* CommandLine: **********
MSI (s) (4C:18) [10:12:20:607]: Note: 1: 2203 2: C:\Windows\system32\config\systemprofile\AppData\LocalLow\Oracle\Java\jre1.8.0_66\jre1.8.0_66.msi 3: -2147287037
MSI (s) (4C:18) [10:12:20:608]: MainEngineThread is returning 3
MSI (s) (4C:F4) [10:12:20:611]: User policy value 'DisableRollback' is 0
MSI (s) (4C:F4) [10:12:20:611]: Machine policy value 'DisableRollback' is 0
MSI (s) (4C:F4) [10:12:20:611]: Incrementing counter to disable shutdown. Counter after increment: 0
MSI (s) (4C:F4) [10:12:20:611]: Note: 1: 1402 2: HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Installer\Rollback\Scripts 3: 2
MSI (s) (4C:F4) [10:12:20:611]: Note: 1: 1402 2: HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Installer\Rollback\Scripts 3: 2
MSI (s) (4C:F4) [10:12:20:611]: Note: 1: 1402 2: HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Installer\InProgress 3: 2
MSI (s) (4C:F4) [10:12:20:611]: Note: 1: 1402 2: HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Installer\InProgress 3: 2
MSI (s) (4C:F4) [10:12:20:611]: Decrementing counter to disable shutdown. If counter >= 0, shutdown will be denied. Counter after decrement: -1
MSI (s) (4C:F4) [10:12:20:612]: Restoring environment variables
MSI (c) (D4:70) [10:12:20:613]: Decrementing counter to disable shutdown. If counter >= 0, shutdown will be denied. Counter after decrement: -1
MSI (c) (D4:70) [10:12:20:613]: MainEngineThread is returning 3
=== Verbose logging stopped: 1/11/2016 10:12:20 ===



REPRODUCIBILITY :
This bug can be reproduced always.

---------- BEGIN SOURCE ----------
You just need to install JRE 1.8.0_66 (x86) on Windows 7 (x64), using the SYSTEM account.
---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
I updated the wrapper so that it installs the extracted MSI to the expected 64 bit path before launching the install