Here's how one family created a deterent.

Or shards of glass mounted to the top of the wall. (Sarcasm)

I'd enclose it fully to the ceiling.

I agree with Kendrah, I'd fully enclose it.

It's an accident waiting to happen.

Don't depend on us for this issue. You must contact your insurance company. A regular home owner's policy will not protect you from accidents or damage caused by a tenant.

The policy you want is called Landlord. The risk policies are entirely different.

Then ask them what to do with the staircase. It is very likely an agent will come to inspect the house and if you haven't fixed the stairway, you won't get insured. When you rent, you must be very cautious about protecting your guests, but also protecting youself.