Tested in chrome # 56.0.2924.87 and Canary #58.0.3013.0 on win 7 and not able to reproduce the issue.Please find the screen shots for your reference.
Steps followed:
1.Added multiple extensions user logged in stage.
2.Close the browser with x
3.Again launched the chrome with out login observed the extensions.

@1000gbps: Could you please let me know if i have missed anything and if possible, provide us with a extensions URL of the issue which would help us to triage the issue further.

Thanks in Advance.

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Ok, trying again - 14 tabs opened, same extensions (ABP, uOrigin, Ghostery, FBPurity)

Nope, again not saved on the same version is 56.0.2924.87 (64-bit). This time and the tabs were not restored

Thank you for providing more feedback. Adding requester "rbasuvula@chromium.org" for another review and adding "Needs-Review" label for tracking.

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

The issue is still here, I'm logged out after restart - now only with two active tabs, same extensions, same version

Tested in chrome # 56.0.2924.87 and Canary #58.0.3027.0 on win 7 and not able to reproduce the issue.Please find the screen shots for your reference.

@1000gbps: Could you please let me know if i have missed anything and if possible, Please check in latest canary build provide us with observation of the issue which would help us to triage the issue further.

Thanks in Advance.

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The issue is still here - same extensions (ABP, uOrigin, Ghostery, FBPurity), 2 wikipedia tabs opened

Google Chrome	56.0.2924.87 (Official Build) (64-bit)
Revision	0e9a9a6f3676ae439b78cd9b3f62b4193c3ac7d5-refs/branch-heads/2924@{#895}
OS	Windows 
JavaScript	V8 5.6.326.50
Flash	24.0.0.221 C:\Users\mobileshit\AppData\Local\Google\Chrome\User Data\PepperFlash\24.0.0.221\pepflashplayer.dll

Thank you for providing more feedback. Adding requester "rbasuvula@chromium.org" to the cc list and removing "Needs-Feedback" label.

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

Unable to reproduce the issue on Win-10 using chrome reported version #56.0.2924.87 and latest canary #59.0.3032.0.

Attached a screen cast for reference.

Following are the steps followed to reproduce the issue.
------------
1. Opened chrome browser and signed into a test account.
2. Added all 4 extensions i.e ABP, uOrigin, Ghostery, FBPurity to chrome.
3. Also opened 2 wikipedia tabs.
4. Closed the browser by clicking the "x" button.
5. Opened the browser and observed that it retained all the extensions and the user also did not log out.

1000gbps@ - Could you please check this issue on latest canary #59.0.3032.0 by creating a new profile without any apps and extensions and please let us know if the issue still persist or not.

Thanks...!!

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No improvement after updating to stable-57.0.2987.98 (64-bit) :(
Well, I already got used to manually login, this thingy arrised when I noticed >1.5GB memory was eaten by the browser and somewhat small sluggish pc performance, and this is fixable only with restarting it ...

Thank you for providing more feedback. Adding requester "krajshree@chromium.org" to the cc list and removing "Needs-Feedback" label.

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1000gbps@: Thank you for your continuous update on this thread, would you mind Uninstall and re-install Chrome freshly if it would fix it.
Before Re-Installing please delete the complete google folder from below path. 
C:\Users\mobileshit\AppData\Local\

Same ... Uninstalled, deleted google folder in \Local\, installed again and the issue is still here

Btw I was blocked from deleting manually npGoogleUpdate3.dll file in C:\Users\mobileshit\AppData\Local\Google\Update\1.3.32.7 even that not a single google related process was started

Thank you for providing more feedback. Adding requester "durga.behera@chromium.org" to the cc list and removing "Needs-Feedback" label.

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

Could anyone from Platform>Extensions please have a look into this issue.

Thanks...!!

Update - issue is still here in version 57.0.2987.133 (64-bit)

Update - my problem is still here in version 60.0.3112.113 (Official Build) 64bit

Update - my problem is still here in version 62.0.3202.62 (Official Build) (64-bit), same OS (Windows 7 Ultimate 64bit)

This time after the last update my last opened tabs were not reopened while before that I must click on 'Recently Opened ... '. Now they are not saved/remembered. Think we are in the same situation where a lot of Firefox versions used by me have the same problem

We are still unable to reproduce the issue on windows 10 & 7 using chrome M62 #62.0.3202.62 .

@Requesting someone from Platform>extensions team to look into this.

Thanks!

Seems version 62.0.3202.75 (Official Build) (64-bit) remembers opened tabs in the "Recently Opened ..." but the main issue with user login state is still here

Unable to reproduce the issue on Win-7 and Win-10 using chrome latest stable #62.0.3202.75 and latest canary #64.0.3253.0.

Attached a screen cast for reference.

Following are the steps followed to reproduce the issue.
------------
1. Opened chrome browser and signed into a test account.
2. Added few extensions
3. Closed the browser by clicking the "x" button.
4. Opened the browser and observed that it retained all the extensions and the user also did not log out.

Could anyone from Platform>Extensions team please have a look into the issue.

Thanks...!!

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As this issue is not able to be reproduced from TE end, hence adding label TE-NeedsTriageHelp and requesting someone from platform>Extensions team to have a look into this and help in further triaging it.

Thanks!

The issue is still here with version 65.0.3325.162 (Official Build) (64-bit)

The issue is still here with version 66.0.3359.181 (Official Build) (64-bit), same extensions. This time test was on freshly installed Windows 7 x64

There's a movement with this issue - on my second machine when I click the user button at the top right corner and choose (one and only) account the browser notifies about that my session will be synced to the account. Version on the both machines is 68.0.3440.106 (Official Build) (64-bit)

The issue is still here with version 69.0.3497.81 (Official Build) (64-bit)

On version 69.0.3497.100 (Official Build) (64-bit) after closing the browser and restarting the machine due to OS updates, the user was logged automatically without additional actions

Please, do not close this issue so I can update the status after the next major Chrome update