Set Chrome to go to last used tab after tab is closed
FLST Chrome(Focus Last Selected Tab) seems to do both of what you're asking.
Feature Set:
- Natural Tab Ordering :: when the selected-tab is closed, Focus goes to the Last-Selected-Tab
- Multiple Window Support :: private tab ordering is maintained for each window
- Tab Migration :: tabs are also tracked when dragged between windows
- Options Page :: right-click the extension icon and select Options
- (Option) Tab-flipping :: flips the current and last tab
- (Option) New Tabs :: switch to the new tab when created
- (Option) Tab Location :: place new tabs on the far-right
PS. I haven't tested this.
I tried the extension mentioned in the answer above and it didn't work for me. It doesn't appear to have that option anymore.
Posting a few alternatives in case someone else wonders here:
Tab Position Customizer 2 - Personally tested and it works as described.
Tab Position Options - Personally tested and it works as described.
Bonus note about one I tried that didn't work:
TabsPlus - There seems to be a bug where the go to last active tab doesn't work if you have multiple windows opened. Since the app hasn't been updated since 2013, I doubt it'll ever work again.