Can they give my old car a ticket if I don’t get a new city sticker even though the car is now totaled?

The city sticker is for insurance.   Instead of replacing the metal plate every year it is cheaper to make stickers and you keep your metal license plate for 5 years.

.   A ticket is issued by a traffic cop because the car is parked somewhere where it shouldn't be (or for some other reason), but the car STILL BELONGS TO YOU. STILL YOUR PROPERTY.  It may be now an EYE SORE TO THE NEIGHBORS OR SOMETHING.   You got to do something with your property.

. No. A new sticker is not the issue. You still are insured.  

THIS IS SOMETHING YOU GOT TO INQUIRE ABOUT THERE, not on line.  The cop that ticketed you knows, or the cop shop does. Ask there for FASTER RESULTS.  I AM IN THE MIDDLE OF A SNOWSTORM RIGHT NOW SO, not in your neighborhood.  World Wide Web only means on the same planet.

So the ticket may be more of a removal notice. The LL does not allow JUNK to be stored on his parking lot without direct approval from him directly. ...so maybe that was a parking lot cop...hired by the LL to patrol the parking to be sure only the tenants park there and that they do not store a wreck there.

. Read your rental contract.  Then talk to your LL to get an extension or get the junk out of here.  Otherwise they will tow it to impound which is a costly place to get the vehicle out of.

Since you didn't tell us what "city" you live in, nobody is going to be able to give you a good answer because we don't know what rules your "city" has.

Nah, you don't need to do anything.  The car will be taken to a salvage yard.  Hopefully, your insurance company will take care of everything, but it doesn't hurt to call and double check.

Yes you do, turn the plates in to show it is not on the road anymore.

If you don't have the car ANY MORE, then you don't need to worry about it.

You DO need to worry about your use of the English language.

What is a city sticker?   You do not have a car anymore.  You do not need a city sticker.

Where in this big world are you talking about? The laws aren't universal. 

FAIL.Try again.