Thank you for your question and I look forward to assisting you. Please keep in mind that I can only respond to your post and the information contained in it, as I do not know what you know unless you have put all of the information in your question. Also, there may be future facts that are as yet undetermined in your matter, that can and must leave some areas of information provided by me broad in nature. However, don't hesitate to ask for clarification if needed! That being said...
It depends. If you fell because of the negligence of your landlord, you have a case for medical bills, wage loss and pain and suffering. However, if your landlord was not at fault, you have no case. Take some pictures and consult with an attorney near you.
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The answer is that it depends and I cannot give you a conclusive answer based upon the facts in your post. If you were still on your landlord's property when you slipped and fell, your landlord may be liable for your injuries. But only if you slipped and injured yourself due to a dangerous condition on the property that your landlord knew or should have known about prior to the accident and failed to repair or warn you about. If that is the case, then your landlord may be liable for your injuries.