You do that, and you'll sterilize the soil underneath. Check with your local extension agent to ask about a cover crop that would be suitable for use as a groundcover.

Actually, covering it with black plastic will never sterilize it, and if you cover the plastic with some bark mulch it won't even get very warm under there. It's not the best solution, but it will be pretty easy to resurrect the soil if you or someone else decides to garden there again.

It's the only option I can think of that wouldn't require any upkeep on the part of the new renters.

Bark on plastic decomposes and hosts weeds. Any part of plastic that becomes exposed is apt to develop tears or holes, with weeds coming through from below. Rocks on top of plastic will hold up much better. However, there will often still be issues with debris getting onto rocks and plastic and forming places for weeds to establish.

Since plastic does not allow air and water through, it does have a deleterious effect on the soil community beneath. And during heavy rains water may run across the top of it, cause debris to accumulate in spots, again forming a substrate for weed growth.

You can avoid the issue of plastic being impermeable by using landscape fabric but the same problems with decomposition of mulch and debris accumulation will still occur. When you establish a cleared area without vegetation the nearby vegetation soon goes about trying to convert this clearing into a vegetated area. In rural areas, especially on wooded sites even asphalt roads soon become invaded if not driven over frequently and maintained with herbicide etc.

Whatever approach is taken some maintenance will have to occur. If there will already be more than a very small amount of mowing on the site it might be just as well to put the area to be converted into lawn also.