Your landlord may be liable, or financially responsible, for your injury. The issue is whether the lack of railing and steepness of stairs would be viewed as unreasonably dangerous by the average person; if so, then a failure to take reasonble steps to reduce the danger (like putting in a railing) might be negligent, and negligence can create liability. If this is the case, the landlord is potentially responsible for your out-of-pocket or unreimbursed medical expenses; lost wages (if any) due to the injury); and for injuries that impair you for some length of time, possibly pain and suffering, too. If the landlord will not voluntarily pay, you would have to sue to seek compensation.